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href="../2261/32-non-right-angled-trigonometry.html">3.2 Non-right angled trigonometry</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../2196/33-applications-of-trigonometry.html">3.3 Applications of trigonometry</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../1862/34-circles.html">3.4 Circles</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../2120/35-36-perpendicular-bisectors-voronoi-diagrams-.html"> 3.5 & 3.6 Perpendicular Bisectors & Voronoi Diagrams </a></label></li></ul></div> <div class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> 3.1 Volume and surface area <a href="#" class="mark-page-favorite pull-right" data-pid="2398" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../mathsapplications.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../1070/geometry-and-trigonometry.html">Geometry and Trigonometry</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">3.1 Volume and surface area</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 30 minutes"><i class="fa fa-clock-o"></i> 30'</span> </ol> <article id="main-article"> <h2><img alt="" src="../../files/GT/vsa/vsa-1.jpg" style="float: left; width: 100px; height: 100px;">3D Shapes</h2> <p>This section is all about the volume and surface area of prisms, cylinders, pyramids, cones and spheres! All of these shapes has their own unique properties and this section is about understanding and calculating the volumes and surface areas.</p> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <p><span id="docs-internal-guid-a27c929b-7fff-4284-6487-5ea9215c6a83"></span></p> <p dir="ltr"><span id="docs-internal-guid-a27c929b-7fff-4284-6487-5ea9215c6a83">In this unit you should learn to…</span></p> <ul style="list-style-type:disc;"> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">work out the volume and surface area of 3 shapes including prisms, cylinders, pyramids, cones and spheres</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">Use the above to solve problems in 3 dimensions</p> </li> </ul> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Slides Gallery - Part 1 - Prisms</p> </div> </div> <div class="panel-body"> <div> <div id="carousel-256" class="dynamic-gallery carousel slide" data-id="256"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos002.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos002.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos003.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos003.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos004.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos004.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos005.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos005.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos006.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos006.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos007.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos007.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos008.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos008.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos009.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos009.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos010.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos010.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos011.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos011.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos012.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos012.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos013.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos013.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos014.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos014.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos015.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos015.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-256/vsa-part-1-nologos001.jpeg" data-fancybox="gallery-256" title="" data-caption=""><img alt="" src="../../../std-galleries/15-256/vsa-part-1-nologos001.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-256" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-256" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos002-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos003-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos004-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos005-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos006-thumb128.jpg"><li><li data-index="5"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos007-thumb128.jpg"><li><li data-index="6"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos008-thumb128.jpg"><li><li data-index="7"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos009-thumb128.jpg"><li><li data-index="8"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos010-thumb128.jpg"><li><li data-index="9"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos011-thumb128.jpg"><li><li data-index="10"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos012-thumb128.jpg"><li><li data-index="11"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos013-thumb128.jpg"><li><li data-index="12"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos014-thumb128.jpg"><li><li data-index="13"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos015-thumb128.jpg"><li><li data-index="14"><img title="Click to view" src="../../../std-galleries/15-256/vsa-part-1-nologos001-thumb128.jpg"><li></li></ol> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>1. What are Prisms</p> </div> </div> <div class="panel-body"> <div> <p>This is a video explaining the different types of prisms and their properties. </p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594557095"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>2. Volume of Prisms</p> </div> </div> <div class="panel-body"> <div> <p>Here we learn about how to use the properties of prisms to calculate their volumes. The video goes through some examples.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594557813"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p> 3.Surface Area of Prisms</p> </div> </div> <div class="panel-body"> <div> <p>Here we learn about calculating surface area by examining the nets of different kinds of prisms.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594558680"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Volume and Surface Area of Cylinders</p> </div> </div> <div class="panel-body"> <div> <p>Here are some slides and videos going over cylinders. Cylinders have the same properties as Prisms, but because the cross section is a circle which is not a straight edge there is a bit of extra thinking to do.</p> <div id="carousel-257" class="dynamic-gallery carousel slide" data-id="257"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-257/vsa-part-2-no-logos001.jpeg" data-fancybox="gallery-257" title="" data-caption=""><img alt="" src="../../../std-galleries/15-257/vsa-part-2-no-logos001.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-257/vsa-part-2-no-logos002.jpeg" data-fancybox="gallery-257" title="" data-caption=""><img alt="" src="../../../std-galleries/15-257/vsa-part-2-no-logos002.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-257/vsa-part-2-no-logos003.jpeg" data-fancybox="gallery-257" title="" data-caption=""><img alt="" src="../../../std-galleries/15-257/vsa-part-2-no-logos003.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-257/vsa-part-2-no-logos004.jpeg" data-fancybox="gallery-257" title="" data-caption=""><img alt="" src="../../../std-galleries/15-257/vsa-part-2-no-logos004.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-257/vsa-part-2-no-logos005.jpeg" data-fancybox="gallery-257" title="" data-caption=""><img alt="" src="../../../std-galleries/15-257/vsa-part-2-no-logos005.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-257" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-257" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-257/vsa-part-2-no-logos001-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-257/vsa-part-2-no-logos002-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-257/vsa-part-2-no-logos003-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-257/vsa-part-2-no-logos004-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/15-257/vsa-part-2-no-logos005-thumb128.jpg"><li></li></ol> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>4. Volume of Cylinders</p> </div> </div> <div class="panel-body"> <div> <p>Here we look at applying the same principles as with prisms to cylinders with their circular base.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594559319"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>5. Surface Area of Cylinders</p> </div> </div> <div class="panel-body"> <div> <p>The nets of cylinders just take a little bit more thought.....</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594560731"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Pyramids and Cones</p> </div> </div> <div class="panel-body"> <div> <p>This section of the page moves on to pyramids and their properties. We will look at calculating their respective volumes and surface areas.</p> <div id="carousel-258" class="dynamic-gallery carousel slide" data-id="258"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos001.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos001.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos002.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos002.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos003.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos003.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos004.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos004.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos005.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos005.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos006.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos006.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos007.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos007.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos008.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos008.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos009.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos009.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos010.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos010.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos011.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos011.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos012.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos012.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos013.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos013.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos014.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos014.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos015.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos015.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-258/vsa-part-3-nologos016.jpeg" data-fancybox="gallery-258" title="" data-caption=""><img alt="" src="../../../std-galleries/15-258/vsa-part-3-nologos016.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-258" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-258" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos001-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos002-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos003-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos004-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos005-thumb128.jpg"><li><li data-index="5"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos006-thumb128.jpg"><li><li data-index="6"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos007-thumb128.jpg"><li><li data-index="7"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos008-thumb128.jpg"><li><li data-index="8"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos009-thumb128.jpg"><li><li data-index="9"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos010-thumb128.jpg"><li><li data-index="10"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos011-thumb128.jpg"><li><li data-index="11"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos012-thumb128.jpg"><li><li data-index="12"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos013-thumb128.jpg"><li><li data-index="13"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos014-thumb128.jpg"><li><li data-index="14"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos015-thumb128.jpg"><li><li data-index="15"><img title="Click to view" src="../../../std-galleries/15-258/vsa-part-3-nologos016-thumb128.jpg"><li></li></ol> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p> 6. What are Pyramids?</p> </div> </div> <div class="panel-body"> <div> <p>Defining the key properties of these shapes and looking at a few different ones.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594562474"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>7. Volume of a Pyramid and Cone</p> </div> </div> <div class="panel-body"> <div> <p>This is calculated by taking a third of the volume of the prism it would fit in. This video shows this in action.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594563070"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>8. Surface Area of a Pyramid</p> </div> </div> <div class="panel-body"> <div> <p>Here we look at the nets of different pyramids so we can see how surface area can be calculated.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594563967"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Cones and Spheres</p> </div> </div> <div class="panel-body"> <div> <p>In this last section we deal with these shapes with curved surface areas, their properties, volume and surface area</p> <div id="carousel-259" class="dynamic-gallery carousel slide" data-id="259"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-259/vsa-part-4-no-logos001.jpeg" data-fancybox="gallery-259" title="" data-caption=""><img alt="" src="../../../std-galleries/15-259/vsa-part-4-no-logos001.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-259/vsa-part-4-no-logos002.jpeg" data-fancybox="gallery-259" title="" data-caption=""><img alt="" src="../../../std-galleries/15-259/vsa-part-4-no-logos002.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-259/vsa-part-4-no-logos003.jpeg" data-fancybox="gallery-259" title="" data-caption=""><img alt="" src="../../../std-galleries/15-259/vsa-part-4-no-logos003.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-259/vsa-part-4-no-logos004.jpeg" data-fancybox="gallery-259" title="" data-caption=""><img alt="" src="../../../std-galleries/15-259/vsa-part-4-no-logos004.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-259/vsa-part-4-no-logos005.jpeg" data-fancybox="gallery-259" title="" data-caption=""><img alt="" src="../../../std-galleries/15-259/vsa-part-4-no-logos005.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-259/vsa-part-4-no-logos006.jpeg" data-fancybox="gallery-259" title="" data-caption=""><img alt="" src="../../../std-galleries/15-259/vsa-part-4-no-logos006.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-259/vsa-part-4-no-logos007.jpeg" data-fancybox="gallery-259" title="" data-caption=""><img alt="" src="../../../std-galleries/15-259/vsa-part-4-no-logos007.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-259/vsa-part-4-no-logos008.jpeg" data-fancybox="gallery-259" title="" data-caption=""><img alt="" src="../../../std-galleries/15-259/vsa-part-4-no-logos008.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-259" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-259" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-259/vsa-part-4-no-logos001-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-259/vsa-part-4-no-logos002-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-259/vsa-part-4-no-logos003-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-259/vsa-part-4-no-logos004-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/15-259/vsa-part-4-no-logos005-thumb128.jpg"><li><li data-index="5"><img title="Click to view" src="../../../std-galleries/15-259/vsa-part-4-no-logos006-thumb128.jpg"><li><li data-index="6"><img title="Click to view" src="../../../std-galleries/15-259/vsa-part-4-no-logos007-thumb128.jpg"><li><li data-index="7"><img title="Click to view" src="../../../std-galleries/15-259/vsa-part-4-no-logos008-thumb128.jpg"><li></li></ol> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p> 9. Surface Area of a Cone</p> </div> </div> <div class="panel-body"> <div> <p>Unpacking the net of a cone is a lovely example of mathematical links. In this video, we explore the links between the variables and show how to calculate this.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594565673"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>10. Volume and Surface Area of a Sphere</p> </div> </div> <div class="panel-body"> <div> <p>The sphere is, in one way, the hardest to deal with, but in another can be done with some startlingly simple formulae!</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594566490"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-violet"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary</p> </div> </div> <div class="panel-body"> <div> <p><em><strong>Revision Cards</strong></em> - Review these condensed 'key point' revision cards to help youn check and keep ideas fresh in your mind.</p> <div id="carousel-275" class="dynamic-gallery carousel slide" data-id="275"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-275/vsa004.jpeg" data-fancybox="gallery-275" title="" data-caption=""><img alt="" src="../../../std-galleries/15-275/vsa004.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-275/vsa005.jpeg" data-fancybox="gallery-275" title="" data-caption=""><img alt="" src="../../../std-galleries/15-275/vsa005.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-275" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-275" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-275/vsa004-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-275/vsa005-thumb128.jpg"><li></li></ol> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <h4>Self Checking quiz</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="tib-quiz" data-stats="15-323-2398"><div class="label label-default q-number">1</div><div class="exercise shadow-bottom"><div class="q-question"><p>a) What is the volume of the cuboid in the diagram below?</p><p>b) What is its surface area?</p><p style="text-align: center;"><img alt="" src="../../files/GT/vsa/q1.jpg" style="width: 250px; height: 240px;"></p></div><div class="q-answer"><p>Write a number only</p><p>a) Volume = <input type="text" style="height: auto;" data-c="60"> <span class="review"></span> cm<sup>3</sup></p><p>b) Surface area = <input type="text" style="height: auto;" data-c="104"> <span class="review"></span> cm<sup>2</sup></p></div><div class="q-explanation"><p>The volume of the base is 5 x 2, then multiply by the height, 6, giveives volume = 5 x 2 x 6</p><p>b) 2 faces are 5 x 2, 2 faces are 6 x 2 and 2 faces are 5 x 6, giving a total of 20 + 24 + 60 = 104cm<sup>2</sup></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><p>....</p><div class="label label-default q-number">2</div><div class="exercise shadow-bottom"><div class="q-question"><p>Drag the correct name of the shape in to the right box.</p><p style="text-align: center;"><img alt="" src="../../files/GT/vsa/which-shape.jpg" style="width: 400px; height: 455px;"></p></div><div class="q-answer"><table border="1" cellpadding="0" cellspacing="0" style="width: 100%;"><tbody><tr><td> Shape A <input type="text" style="height: auto;" data-c="Triangular Prism"> <span class="review"></span></td><td><span class="q-text-draggable draggable" draggable="true">Triangular prism</span> <span class="q-text-draggable draggable" draggable="true">Pyramid</span></td></tr><tr><td>Shape B <input type="text" style="height: auto;" data-c="Cylinder"> <span class="review"></span> </td><td><span class="q-text-draggable draggable" draggable="true">Cylinder</span> <span class="q-text-draggable draggable" draggable="true">Cone</span></td></tr><tr><td>Shape C<span style="background-color: rgb(235, 244, 250);"> <input type="text" style="height: auto;" data-c="Cuboid"> <span class="review"></span> </span></td><td><span class="q-text-draggable draggable" draggable="true">Cuboid</span> <span class="q-text-draggable draggable" draggable="true">Octangonal based pyramid</span></td></tr><tr><td><table border="1" cellpadding="0" cellspacing="0" style="width: 100%;"><tbody><tr><td>Shape D <input type="text" style="height: auto;" data-c="Rectangular based Pyramid"> <span class="review"></span> </td><td> </td></tr></tbody></table></td><td><span class="q-text-draggable draggable" draggable="true">Rectangular based Pyramid</span> <span class="q-text-draggable draggable" draggable="true">Sphere</span></td></tr></tbody></table></div><div class="q-explanation"> </div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><p>....</p><div class="label label-default q-number">3</div><div class="exercise shadow-bottom"><div class="q-question"><p>The following right angled triangle is one face of a triangular prism whose length is 12 cm....</p><p><img alt="" src="../../files/GT/vsa/q3.jpg" style="width: 200px; height: 177px; float: left;"></p><p>a) Calculate the length of the hypotenuse of the triangle</p><p>b) What is the area of the triangular cross section?</p><p>c) What is the volume of the prism?</p><p>d) What is the total surface area of the prism?</p><p> </p></div><div class="q-answer"><p>Write numbers only</p><p>a) Length of hypotenuse is <input type="text" style="height: auto;" data-c="5"> <span class="review"></span> cm</p><p>b) The area of the triangular cross section is <input type="text" style="height: auto;" data-c="6"> <span class="review"></span> cm<sup>2</sup></p><p>c) The volume of the prism is <input type="text" style="height: auto;" data-c="72"> <span class="review"></span> cm<sup>3</sup></p><p>d)The total surface area of the prism is <input type="text" style="height: auto;" data-c="156"> <span class="review"></span> cm<sup>2</sup></p></div><div class="q-explanation"><p>a) Using pythagoras theorem, h<sup>2</sup> = 3<sup>2</sup> + 4<sup>2</sup></p><p>b) Area = (3 x 4)/2 = 6</p><p>c) Volume is corss sectional area x length, so V = 6 x 12 = 72</p><p>d) There are 5 faces, 2 triangles on each end each 6, the bottom which is 3 x 12, the back which is 4 x 12 and the sloping face which is 5 x 12, so 6 + 6 + 36 + 48 + 60 = 156</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><p>....</p><div class="label label-default q-number">4</div><div class="exercise shadow-bottom"><div class="q-question"><p>A triangular prism has a volume of 300 cm<sup>3</sup> and a length of 15cm.</p><p>a) What is the area of the triangular cross section?</p><p>b) If the triangular corss section has a height of 5cm, how long is its base?</p></div><div class="q-answer"><p>a) Area of triangular face is <input type="text" style="height: auto;" data-c="20"> <span class="review"></span> cm<sup>2</sup></p><p>b) the base of the triangular criss section is <input type="text" style="height: auto;" data-c="8"> <span class="review"></span> cm</p></div><div class="q-explanation"><p>a) Volume = Cross section x length, so 300 = Cross section x 15. Cross section = 300/15</p><p>b) Area of truiangle is base x height / 2. If base x 5/2 = 20 then base must be 8</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><p>...</p><div class="label label-default q-number">5</div><div class="exercise shadow-bottom"><div class="q-question"><p>Consider the following cylinder with a radius of 7 cm and a heigth of 15 cm</p><p><img alt="" src="../../files/GT/vsa/q5.jpg" style="width: 234px; height: 316px; float: left;"></p><p>a) Work out the volume of the cylinder</p><p>b) Work out the surface are of the cylinder</p><p>Give your answers to 3sf</p></div><div class="q-answer"><p>a) Volume = <input type="text" style="height: auto;" data-c="2040"> <span class="review"></span> cm<sup>3</sup></p><p>b) Surface area = <input type="text" style="height: auto;" data-c="4930"> <span class="review"></span> cm<sup>2</sup></p></div><div class="q-explanation"><p>a) Volume of a cylinder = (pi)r<sup>2</sup>h. in this case pi x 7<sup>2 </sup>x 15 = 2039.07060 which is 2040 to 3sf</p><p>b) Surface area of a cylinder = 2 (pi)r<sup>2</sup> + 2(pi)rh, substitute r = 7 and h = 15 and you get SA = 4926.01728 which rounds to 4930 to 3sf</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><p>....</p><div class="label label-default q-number">6</div><div class="exercise shadow-bottom"><div class="q-question"><p>Consider the following rectangular based Pyramid and its net. CD = 4cm, BC = 2cm, EF = 3cm</p><p style="text-align: center;"><img alt="" src="../../files/GT/vsa/q5b.jpg" style="width: 307px; height: 275px;"><img alt="" src="../../files/GT/vsa/q5c.jpg" style="width: 325px; height: 275px;"></p><p>a) Work out the volume of the pyramid</p><p>b) What is the perpendicualr height, h, of triangle ECD? (give answer to 3sf)</p><p>c) What is the perpendicualr height, p, of triangle EBC? (give answer to 3sf)</p><p>d) Calculate the surface area of the Pyramid using rounded answers to the previous questions</p></div><div class="q-answer"><p>a) V = <input type="text" style="height: auto;" data-c="8"> <span class="review"></span> cm<sup>3</sup></p><p>b) h = <input type="text" style="height: auto;" data-c="3.16"> <span class="review"></span> cm</p><p>c) p = <input type="text" style="height: auto;" data-c="3.61"> <span class="review"></span> cm</p><p>d) SA = <input type="text" style="height: auto;" data-c="27.9"> <span class="review"></span> cm<sup>2</sup></p></div><div class="q-explanation"><p>a) <span class="math-tex">\(V=\frac { 1 }{ 3 } Area\quad of\quad base\quad \times \quad heigth\\ V\quad =\quad \frac { 2\times 4\times 3 }{ 3 } =8{ cm }^{ 3 }\)</span></p><p>b) Consider m to be the midpoint of CD then we have the folllowing triangle</p><p><img alt="" src="../../files/GT/vsa/q5d.jpg" style="width: 150px; height: 130px; float: left;">The vertical height of triangle ECD is</p><p><span class="math-tex">\(h\quad =\quad \sqrt { { 3 }^{ 2 }+{ 1 }^{ 2 } } \\ h\quad =\quad 3.162277\\ h\quad =\quad 3.16\quad cm\quad (3sf)\)</span></p><hr class="hidden-separator"><p>c) Consider n to be the midpoint of BC then we have the folllowing triangle</p><p><img alt="" src="../../files/GT/vsa/q5e.jpg" style="float: left; width: 130px; height: 130px;">The vertical height of triangle EBC is</p><p><span class="math-tex">\(p\quad =\quad \sqrt { { 3 }^{ 2 }+{ 2 }^{ 2 } } \\ p\quad =\quad 3.605551\\ p\quad =\quad 3.61\quad cm\quad (3sf)\)</span></p><hr class="hidden-separator"><p>d) <span class="math-tex">\(Base\quad area\quad =\quad 2\quad x\quad 4\quad =\quad 8{ cm }^{ 2 }\\ \\ Triangle\quad ECD\quad =\quad triangle\quad EBA\quad \\ Area\quad =\quad \frac { 3.16\times 4 }{ 2 } =\quad 6.32\\ \\ Triangle\quad EBC\quad =\quad triangle\quad EAD\quad \\ Area\quad =\quad \frac { 3.61\times 2 }{ 2 } =\quad 3.61\\ \\ Total\quad surface\quad area\quad =\quad 8\quad +\quad 2\times 6.32\quad +\quad 2\times 3.61\quad =\quad 27.86\quad { cm }^{ 2 }\quad \\ \\ \)</span></p><p>SA = 27.9 (3sf)</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><p>...</p><div class="label label-default q-number">7</div><div class="exercise shadow-bottom"><div class="q-question"><p>Calculate a) the volume and b) the surface area of a cone with a base radius of 5cm and a height 12cm</p></div><div class="q-answer"><p>a) Volume = <input type="text" style="height: auto;" data-c="314"> <span class="review"></span> cm<sup>3</sup></p><p>b) Surface area = <input type="text" style="height: auto;" data-c="283"> <span class="review"></span> cm<sup>2</sup></p></div><div class="q-explanation"><p>a) <span class="math-tex">\(Volume\quad of\quad a\quad cone\quad =\quad \frac { \pi { r }^{ 2 }h }{ 3 } \\ V\quad =\quad \frac { \pi { \quad \times \quad 5 }^{ 2 }\quad \times \quad 12 }{ 3 } \\ V\quad =\quad 314.15926\\ V\quad =\quad 314\quad { cm }^{ 3 }\\ \\ \)</span></p><p>b)<img alt="" src="../../files/GT/vsa/q7.jpg" style="float: left; width: 130px; height: 141px;"> The profile of the cone looks like the diagram to the left. the slant height, l is calculated....</p><p><span class="math-tex">\(Slant\quad height\quad of\quad a\quad cone,\quad l\\ l\quad =\quad \sqrt { { 5 }^{ 2 }+{ 12 }^{ 2 } } \\ l\quad =\quad \sqrt { 169 } \\ l\quad =\quad 13\quad cm\\ \\ \\ \)</span></p><p><span class="math-tex">\(Surface\quad area\quad of\quad a\quad cone\quad =\quad \pi { r }^{ 2 }+\pi rl\\ SA\quad =\quad \pi \quad \times \quad 25\quad +\quad \pi \quad \times \quad 5\quad \times \quad 13\\ SA\quad =\quad 282.7433\\ SA\quad =\quad 283\quad { cm }^{ 2 }\)</span></p><hr class="hidden-separator"></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">8</div><div class="exercise shadow-bottom"><div class="q-question"><p><img alt="" src="../../files/GT/vsa/q3.jpg" style="float: left; width: 200px; height: 177px;">The right angled triangle on the left is the base of a right pyramid whose volume is 90 cm<sup>3</sup>. What is the height of the pyramid?</p></div><div class="q-answer"><p>Height = <input type="text" style="height: auto;" data-c="45"> <span class="review"></span> cm</p></div><div class="q-explanation"><p><span class="math-tex">\(Volume\quad of\quad pyramid\quad =\quad \frac { 1 }{ 3 } Area\quad of\quad base\quad \times \quad height\quad \\ 90\quad =\quad \frac { 1 }{ 3 } \quad \times \quad 6\quad \times \quad h\\ 270\quad =\quad 6h\\ h\quad =\quad \frac { 270 }{ 6 } \quad =\quad 45cm\\ \\ \\ \)</span></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">9</div><div class="exercise shadow-bottom"><div class="q-question"><p>What is a) the volume and b) the surface area of a Sphere with a radius of 10cm? Give answers to 3sf</p></div><div class="q-answer"><p>a) Volume = <input type="text" style="height: auto;" data-c="4190"> <span class="review"></span> cm<sup>3</sup></p><p>b) Surface Area = <input type="text" style="height: auto;" data-c="1260"> <span class="review"></span> cm<sup>2</sup></p></div><div class="q-explanation"><p>a) <span class="math-tex">\(Volume\quad of\quad sphere\quad =\quad \frac { 4 }{ 3 } \pi { r }^{ 3 }\\ V\quad =\quad \frac { 4 }{ 3 } \pi \quad \times \quad 10^{ 3 }\\ V\quad =\quad 4188.7902\\ V\quad =\quad 4190\quad { cm }^{ 3 }\quad (3sf)\\ \\ \\ \)</span></p><p>b) <span class="math-tex">\(Surface\quad Area\quad of\quad sphere\quad =\quad 4\pi { r }^{ 2 }\\ SA\quad =\quad 4\pi { \quad \times \quad 10 }^{ 2 }\\ SA\quad =\quad 1256.6370\\ SA\quad =\quad 1260\quad { cm }^{ 2 }\quad (3sf)\\ \\ \\ \)</span></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">10</div><div class="exercise shadow-bottom"><div class="q-question"><p>A sphere and a cone have the same radius, 7cm, and the same volume. What is the height of the cone? Do not round until your final answer then give your answer to 3sf.</p></div><div class="q-answer"><p>Height of cone = <input type="text" style="height: auto;" data-c="28.0"> <span class="review"></span> cm</p></div><div class="q-explanation"><p><span class="math-tex">\(Volume\quad of\quad sphere\quad =\quad \frac { 4 }{ 3 } \pi { r }^{ 3 }\\ { V }_{ sphere }\quad =\quad \frac { 4 }{ 3 } \pi \quad \times \quad 7^{ 3 }\\ { V }_{ sphere }\quad =\quad 1436.7550402\quad (Keep\quad calculator\quad display)\\ \\ { V }_{ sphere }\quad =\quad { V }_{ cone\quad }=\quad \frac { 1 }{ 3 } \pi { r }^{ 2 }h\quad =\quad \frac { 1 }{ 3 } \pi { \quad \times \quad 7 }^{ 2 }h\\ (\times 3)\quad \quad \quad 3\quad \times \quad { V }_{ sphere }\quad =\quad \pi { \quad \times \quad 49 }h\\ (\div 49\pi )\quad \frac { 3\quad \times \quad { V }_{ sphere } }{ 49\pi } \quad =\quad h\\ h\quad =\quad 27.99999999\\ h\quad =\quad 28.0\quad cm\quad (3sf)\\ \\ \)</span></p></div><div class="actions"><span class="score" 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