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<h2 class="wp-block-heading">Key Concepts</h2>



<ul class="wp-block-list">
<li>Find the number of unit cubes.</li>



<li>Find volumes of <a href="https://www.turito.com/learn/math/prisms-and-cylinders-volume-grade-9">prisms and cylinders</a>.</li>
</ul>



<h3 class="wp-block-heading">Introduction</h3>



<h4 class="wp-block-heading">Volume</h4>



<p>Volume is the number of cubic units contained in a solid. It is measured in cubic units.&nbsp;&nbsp;</p>



<p>The basic formula is V = Bh, where B = area of the base, h = height.&nbsp;</p>



<h4 class="wp-block-heading">Cubic Unit</h4>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3028.png" alt="Cubic Unit: " class="wp-image-19011" style="width:405px;height:195px" width="405" height="195" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3028.png 781w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3028-300x144.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3028-768x369.png 768w" sizes="auto, (max-width: 405px) 100vw, 405px" /></figure></div>


<h4 class="wp-block-heading">Find the number of unit cubes&nbsp;</h4>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3029.png" alt="Volume of a cube postulate" class="wp-image-19012" style="width:510px;height:129px" width="510" height="129" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3029.png 605w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3029-300x76.png 300w" sizes="auto, (max-width: 510px) 100vw, 510px" /></figure></div>


<p><strong>Example 1:</strong><strong>&nbsp;</strong>&nbsp;</p>



<p>Find the volume of the puzzle piece shown in cubic units.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3024.png" alt="Example 1:  " class="wp-image-19002" style="width:344px;height:233px" width="344" height="233" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3024.png 394w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3024-300x203.png 300w" sizes="auto, (max-width: 344px) 100vw, 344px" /></figure></div>


<p><strong>Solution:</strong>&nbsp;</p><div class="fillWidthInMob"><a loading='lazy' class="showAdInAllRes"  data-toggle="modal" data-target=#homeLeadForm data-heading="Get Expert Guidance" href="#"><img class="img-fluid" alt="parallel" src=https://a.storyblok.com/f/128066/1100x230/00b28b4876/11-applying-for-collages_leaderboard-1100x230.jpg /></a></div>



<p>To find the volume, find the number of unit cubes it contains. Separate the piece into three rectangular boxes as follows:&nbsp;&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="394" height="273" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3127.png" alt="Example 1: Solution " class="wp-image-19169" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3127.png 394w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3127-300x208.png 300w" sizes="auto, (max-width: 394px) 100vw, 394px" /></figure></div>


<p>The base is 3 units by 1 unit. So, it contains 3 × 1, or 3 unit cubes.&nbsp;&nbsp;</p>



<p>The top layer is 3 units by 1 unit. So, it contains 3 × 1, or 3 unit cubes.&nbsp;&nbsp;</p>



<p>The upper left box is 1 unit by 1 unit1. So, it contains 1 × 1, or 1 unit cube.&nbsp;&nbsp;</p>



<p>By the Volume Addition Postulate, the total volume of the puzzle piece is 3 + 3 + 1 = 7 cubic units.&nbsp;</p><div class="fillWidthInMob"><a loading='lazy' class="showAdInAllRes"  data-toggle="modal" data-target=#homeLeadForm data-heading="Get Expert Guidance" href="#"><img class="img-fluid" alt="parallel" src=https://a.storyblok.com/f/128066/1100x230/00b28b4876/11-applying-for-collages_leaderboard-1100x230.jpg /></a></div>



<p><strong>Example 2:</strong>&nbsp;</p>



<p>Find the volume of the solid in cubic units.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="360" height="303" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3025.png" alt="Example 2: " class="wp-image-19004" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3025.png 360w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3025-300x253.png 300w" sizes="auto, (max-width: 360px) 100vw, 360px" /></figure></div>


<p><strong>Solution:</strong>&nbsp;</p>



<p>To find the volume, find the number of unit cubes it contains. Separate the piece into three rectangular boxes as follows:&nbsp;</p>



<p><strong>Front Layer:&nbsp;</strong></p>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3026.png" alt="Front Layer: " class="wp-image-19007" style="width:226px;height:306px" width="226" height="306" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3026.png 270w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3026-222x300.png 222w" sizes="auto, (max-width: 226px) 100vw, 226px" /></figure></div>


<p><strong>Middle Layer:&nbsp;</strong></p>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3030.png" alt="Middle Layer: " class="wp-image-19014" style="width:222px;height:272px" width="222" height="272" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3030.png 270w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3030-245x300.png 245w" sizes="auto, (max-width: 222px) 100vw, 222px" /></figure></div>


<p><strong>Back Layer:</strong>&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3026.png" alt="Front Layer: " class="wp-image-19005" style="width:215px;height:290px" width="215" height="290" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3026.png 270w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3026-222x300.png 222w" sizes="auto, (max-width: 215px) 100vw, 215px" /></figure></div>


<p>By the Volume Addition Postulate, the total volume of the solid is 11 + 11 + 11 =33 cubic units.&nbsp;</p>



<h3 class="wp-block-heading">Find volumes of prisms and cylinders&nbsp;</h3>



<h4 class="wp-block-heading">Volume of a prism</h4>



<p>The volume of a right <a href="https://www.turito.com/learn/math/volume-of-rectangular-prism" data-type="link" data-id="https://www.turito.com/learn/math/volume-of-rectangular-prism">rectangular prism</a> is equal to the product of the height and the area of the base.&nbsp;</p>



<p>V = Bh&nbsp;</p>



<p>Where B is the area of the base and <em>h</em> is the height.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3031.png" alt="Volume of a prism" class="wp-image-19015" style="width:539px;height:237px" width="539" height="237" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3031.png 804w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3031-300x132.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3031-768x338.png 768w" sizes="auto, (max-width: 539px) 100vw, 539px" /></figure></div>


<h4 class="wp-block-heading">Volume of a Cylinder</h4>



<p>The <a href="https://www.turito.com/learn/math/volume-of-cylinder" data-type="link" data-id="https://www.turito.com/learn/math/volume-of-cylinder">volume of a cylinder</a> is equal to the product of the height and the area of the base.&nbsp;</p>



<p>V = Bh = πr<sup>2</sup>h&nbsp;</p>



<p>Where B is the area of the base, <em>h</em> is the height, and <em>r</em> is the radius of the base.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="388" height="264" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3027.png" alt="Volume of a cylinder: " class="wp-image-19009" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3027.png 388w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3027-300x204.png 300w" sizes="auto, (max-width: 388px) 100vw, 388px" /></figure></div>


<p><strong>Example 3:</strong>&nbsp;</p>



<p>Find the volume of the following triangular prism.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3032.png" alt="Example 3: " class="wp-image-19016" style="width:233px;height:185px" width="233" height="185" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3032.png 439w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3032-300x238.png 300w" sizes="auto, (max-width: 233px) 100vw, 233px" /></figure></div>


<p><strong>Solution:</strong>&nbsp;</p>



<p>The area of a base is ½ (10)(8) = 40 and l = 3.&nbsp;</p>



<p>V = Area of a base x l&nbsp;</p>



<p>V = 40(3) = 120 cubic units&nbsp;</p>



<p><strong>Example 4</strong>:</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="205" height="319" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3033.png" alt="Example 4:" class="wp-image-19017" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3033.png 205w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3033-193x300.png 193w" sizes="auto, (max-width: 205px) 100vw, 205px" /></figure></div>


<p>A soda can measures 5.5 inches high, and its diameter is 2.5 inches. Find the&nbsp; approximate volume.&nbsp;</p>



<p><strong>Solution:</strong>&nbsp;</p>



<p>The diameter is 2.5 in. The radius is 2.5 ÷ 2 inches.&nbsp;</p>



<p>V = pr<sup>2</sup>h&nbsp;</p>



<p>V = p(1.25<sup>2</sup>)(5.5)&nbsp;</p>



<p>V » 26.98 in<sup>3</sup>&nbsp;</p>



<h2 class="wp-block-heading">Exercise</h2>



<ol class="wp-block-list" type="1">
<li>Explain in your own words how to find the volume of a figure. Give an example.</li>



<li>Find the volume of the given cube</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3040.png" alt="Find the volume of the given cube" class="wp-image-19024" style="width:344px;height:229px" width="344" height="229" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3040.png 401w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3040-300x200.png 300w" sizes="auto, (max-width: 344px) 100vw, 344px" /></figure></div>


<ol class="wp-block-list" start="3">
<li>Find the volume of the figure.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3042.png" alt="Find the volume of the figure." class="wp-image-19026" style="width:204px;height:201px" width="204" height="201"/></figure></div>


<ol class="wp-block-list" start="4">
<li>Find the volume of the figure.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3044.png" alt="Find the volume of the figure." class="wp-image-19028" style="width:223px;height:240px" width="223" height="240"/></figure></div>


<ol class="wp-block-list" start="5">
<li>Find the volume of the figure.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3047.png" alt="Find the volume of the figure." class="wp-image-19031" style="width:241px;height:190px" width="241" height="190"/></figure></div>


<ol class="wp-block-list" start="6">
<li>Find the volume of the figure.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3048.png" alt="Find the volume of the figure." class="wp-image-19032" style="width:290px;height:250px" width="290" height="250" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3048.png 340w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3048-300x259.png 300w" sizes="auto, (max-width: 290px) 100vw, 290px" /></figure></div>


<ol class="wp-block-list" start="7">
<li>Find the volume of the figure.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3049.png" alt="Find the volume of the figure." class="wp-image-19033" style="width:415px;height:217px" width="415" height="217" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3049.png 491w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3049-300x157.png 300w" sizes="auto, (max-width: 415px) 100vw, 415px" /></figure></div>


<ol class="wp-block-list" start="8">
<li>A birthday cake has three layers. The top cake has a diameter of 8 inches and is 3 inches deep. The middle cake is 12 inches in diameter and is 4 inches deep. The bottom cake is 14 inches in diameter and is 6 inches deep. Find the volume of the entire cake, ignoring the icing.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="217" height="278" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3050.png" alt="A birthday cake has three layers. The top cake has a diameter of 8 inches and is 3 inches deep. The middle cake is 12 inches in diameter and is 4 inches deep. The bottom cake is 14 inches in diameter and is 6 inches deep. Find the volume of the entire cake, ignoring the icing." class="wp-image-19034"/></figure></div>


<ol class="wp-block-list" start="9">
<li>Find the volume of a square prism that has a base edge length of 5 feet and a height of 12 feet.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3051.png" alt="Find the volume of a square prism that has a base edge length of 5 feet and a height of 12 feet." class="wp-image-19035" style="width:230px;height:232px" width="230" height="232" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3051.png 266w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3051-150x150.png 150w" sizes="auto, (max-width: 230px) 100vw, 230px" /></figure></div>


<ol class="wp-block-list" start="10">
<li>Find the volume of the solid prism shown below.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3053.png" alt="Find the volume of the solid prism shown below." class="wp-image-19037" style="width:346px;height:303px" width="346" height="303" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3053.png 445w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3053-300x263.png 300w" sizes="auto, (max-width: 346px) 100vw, 346px" /></figure></div>


<h3 class="wp-block-heading">Concept Map</h3>


<div class="wp-block-image">
<figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3058-1024x318.png" alt="Concept Map:  " class="wp-image-19043" style="width:682px;height:211px" width="682" height="211" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3058-1024x318.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3058-300x93.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3058-768x238.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3058.png 1302w" sizes="auto, (max-width: 682px) 100vw, 682px" /></figure></div>


<h3 class="wp-block-heading">What have we learned</h3>



<ul class="wp-block-list">
<li>Find the number of unit cubes in the given solid shape.</li>



<li>Find volume of a prism by using the formula.</li>



<li>Find volume of a cylinder by using the formula.</li>
</ul>
