<h2>Volume of Prisms and Cylinders</h2>
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<h3>Definition: Volume</h3>
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<p>Volume is the three dimensional space occupied by an object, or the contents of an object. It is measured in cubic units.</p>
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<p>The volume of right prisms and cylinders is simply calculated by multiplying the area of the base of the solid by the height of the solid.</p>
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<p>The video below shows several examples of calculating the volume of a right prism.</p>
<iframe allowfullscreen="allowfullscreen" frameborder="0" height="360" src="https://www.youtube.com/embed/ZqzAOZ9pP9Q?rel=0&amp;modestbranding=1&amp;cc_lang_pref=en&amp;cc_load_policy=1" width="640"></iframe></div>
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<p><strong>Rectangular prism</strong></p>
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<td style="width: 293px;"><img alt="2cd04c92e584166cc32f0dfff11e3ce8.png" src="https://data.ulearngo.com/assets/59de1a71-dd6a-4efe-85ce-bc6eca6ef99d"/></td>
<td style="width: 600px;">$\begin{array}{rl} \text{Volume}&amp; =\text{area of base}\times \text{height} \\ &amp; =\text{area of rectangle}\times \text{height} \\ &amp; =l\times b\times h \end{array}$</td>
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<p><strong>Triangular prism</strong></p>
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<td style="width: 293px;"><img alt="b1c06d8cb93bc6d94eb3aae3dcdc3987.png" src="https://data.ulearngo.com/assets/9fc14817-234f-42e6-a1b1-cc791e624882"/></td>
<td style="width: 600px;">$\begin{array}{rl} \text{Volume}&amp; =\text{area of base}\times \text{height} \\ &amp; =\text{area of triangle}\times \text{height} \\ &amp; =\left(\cfrac{1}{2}b\times h)\times H \end{array}$</td>
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<p><strong>Cylinder</strong></p>
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<td style="width: 293px;"><img alt="e12f4a370695c4995caef7119cf0a7b5.png" src="https://data.ulearngo.com/assets/e463c575-251b-49b6-9c38-369e4be14ea3"/></td>
<td style="width: 600px;">$\begin{array}{rl} \text{Volume}&amp; =\text{area of base}\times \text{height} \\ &amp; =\text{area of circle}\times \text{height} \\ &amp; =\pi {r}^{2}\times h \end{array}$</td>
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<h2>Example</h2>
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<h3>Question</h3>
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<p>Find the volume of the following cube:</p>
<img alt="45c8ed78d3cbfae5304d137843dad685.png" src="https://data.ulearngo.com/assets/79d2aa2d-caef-4da1-9ad8-a6243177aab1"/></div>
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<h3>Find the area of the base</h3>

\begin{align*} \text{area of square} &amp; = {s}^{2} \\ &amp; = {3}^{2} \\ &amp; = \text{9}\text{ cm$^{2}$} \end{align*}</div>
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<h3>Multiply the area of the base by the height of the solid to find the volume</h3>

\begin{align*} \text{volume} &amp; = \text{area of base}\times \text{height} \\ &amp; = 9\times 3 \\ &amp; = \text{27}\text{ cm$^{3}$} \end{align*}</div>
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<h3>Write the final answer</h3>
<p>The volume of the cube is $\text{27}$ $\text{cm$^{3}$}$.</p>
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<h2>Example</h2>
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<h3>Question</h3>
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<p>Find the volume of the triangular prism:</p>
<img alt="cefbea445e2194f29d47767c201fcdb1.png" src="https://data.ulearngo.com/assets/c78deb21-699b-4992-87d7-9615b880af1d"/></div>
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<h3>Find the area of the base</h3>

\begin{align*} \text{area of triangle} &amp; = \cfrac{1}{2}b\times h \\ &amp; = (\cfrac{1}{2}\times 8)\times 10 \\ &amp; = \text{40}\text{ cm$^{2}$} \end{align*}</div>
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<h3>Multiply the area of the base by the height of the solid to find the volume</h3>

\begin{align*} \text{volume}&amp; =\text{area of base}\times \text{height} \\ &amp; = \cfrac{1}{2}b\times h\times H \\ &amp; = 40\times 20 \\ &amp; = \text{800}\text{ cm$^{3}$} \end{align*}</div>
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<h3>Write the final answer</h3>
<p>The volume of the triangular prism is $\text{800}$ $\text{cm$^{3}$}$.</p>
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<h2>Example</h2>
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<h3>Question</h3>
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<p>Find the volume of the following cylinder (correct to 1 decimal place):</p>
<img alt="62891bea8972b49da1b3664b90c303b6.png" src="https://data.ulearngo.com/assets/c393ceef-bb3c-45c7-aa2a-66d111f9fd42"/></div>
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<h3>Find the area of the base</h3>

\begin{align*} \text{area of circle}&amp; =\pi {r}^{2} \\ &amp; =\pi {(4)}^{2} \\ &amp; = 16\pi ~\text{cm$^{2}$} \end{align*}</div>
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<h3>Multiply the area of the base by the height of the solid to find the volume</h3>

\begin{align*} \text{volume}&amp; =\text{area of base}\times \text{height} \\ &amp; =\pi {r}^{2}\times h \\ &amp; =16\pi \times 15 \\ &amp; \approx \text{754.0}\text{ cm$^{3}$} \end{align*}</div>
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<h3>Write the final answer</h3>
<p>The volume of the cylinder is $\text{754.0}$ $\text{cm$^{3}$}$.</p>
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Volume of Prisms and Cylinders

Mathematics studies measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are popular topics in mathematics.

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Explore how to calculate area, surface area, and volume of various geometric shapes including polygons, prisms, cones, pyramids, and spheres in this tutorial.


Volume of Prisms and Cylinders

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