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Pre-Algebra : Volume

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Example Questions

Example Question #1 : Volume Of A Cylinder

A cylinder has a radius of 4 inches and a height of 5 inches. What is the volume of the cylinder?

Possible Answers:

$\small 40\pi$ $\displaystyle \small 40\pi$

$\small 80\pi$ $\displaystyle \small 80\pi$

$\small 20\pi$ $\displaystyle \small 20\pi$

$\small 80$ $\displaystyle \small 80$

$\small 100\pi$ $\displaystyle \small 100\pi$

Correct answer:

$\small 80\pi$ $\displaystyle \small 80\pi$

Explanation:

The formula for the volume of the cylinder is $\small V=\pi r^2h$ $\displaystyle \small V=\pi r^2h$, where $\small r$ $\displaystyle \small r$ is the radius and $\small h$ $\displaystyle \small h$ is the height. Plug in the lengths we are given to solve:

$\small V=\pi r^2h$ $\displaystyle \small V=\pi r^2h$

$\small V = \pi (4)^2(5)$ $\displaystyle \small V = \pi (4)^2(5)$

$\small V=\pi 16(5)$ $\displaystyle \small V=\pi 16(5)$

$\small V = 80\pi$ $\displaystyle \small V = 80\pi$

The cylinder has a volume of $80\pi$ $\displaystyle 80\pi$.

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Example Question #2 : Volume Of A Cylinder

What is the volume of a cylinder with a height of 20 and a radius of 10?

Possible Answers:

$\small \small 2000\pi$ $\displaystyle \small \small 2000\pi$

$\small 2000$ $\displaystyle \small 2000$

$\small 4000\pi$ $\displaystyle \small 4000\pi$

$\small 500$ $\displaystyle \small 500$

$\small 500\pi$ $\displaystyle \small 500\pi$

Correct answer:

$\small \small 2000\pi$ $\displaystyle \small \small 2000\pi$

Explanation:

The volume of a cylinder is given by the formula:

$\small \small volume=radius^2*height\ast \pi$ $\displaystyle \small \small volume=radius^2*height\ast \pi$

with $\small height = 20$ $\displaystyle \small height = 20$ and $\small radius = 10$ $\displaystyle \small radius = 10$, the equation is:

$\small volume = 10^2 * 20\ast \pi$ $\displaystyle \small volume = 10^2 * 20\ast \pi$,

Thus, $\small volume = 100* 20\ast \pi$ $\displaystyle \small volume = 100* 20\ast \pi$, or $\small 2000\pi$ $\displaystyle \small 2000\pi$

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Example Question #1 : Volume Of A Cylinder

What is the volume of a cylinder with a diameter equal to $\displaystyle 6$ and height equal to $\displaystyle 8$?

Possible Answers:

$72\pi$ $\displaystyle 72\pi$

$36\pi$ $\displaystyle 36\pi$

$288\pi$ $\displaystyle 288\pi$

$144\pi$ $\displaystyle 144\pi$

Correct answer:

$72\pi$ $\displaystyle 72\pi$

Explanation:

If the diameter is 6, then the radius is half of 6, or 3.

Plug this radius into the formula for the volume of a cylinder:

$V=hr^2\pi=(8)(3^2)\pi=(8)(9)\pi=72\pi$ $\displaystyle V=hr^2\pi=(8)(3^2)\pi=(8)(9)\pi=72\pi$

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Example Question #1 : Volume Of A Cylinder

Find the volume of the cylinder.

Jared buys a can of chicken noodle soup for dinner. The height of the can is $6\:in$ $\displaystyle 6\:in$. The radius of the can is $2\:in$ $\displaystyle 2\:in$. What is the volume of the can?

Possible Answers:

$12\pi\:in^3$ $\displaystyle 12\pi\:in^3$

$6\pi\:in^3$ $\displaystyle 6\pi\:in^3$

$72\pi\:in^3$ $\displaystyle 72\pi\:in^3$

$22\pi\:in^3$ $\displaystyle 22\pi\:in^3$

$24\pi\:in^3$ $\displaystyle 24\pi\:in^3$

Correct answer:

$24\pi\:in^3$ $\displaystyle 24\pi\:in^3$

Explanation:

The correct answer to the question is $24\pi\:in^3$ $\displaystyle 24\pi\:in^3$.

We know that a can is a cylinder. We also know that the formula for the volume of a cylinder is $\pi r^{^{2}}h$ $\displaystyle \pi r^{^{2}}h$.

Plug in the numbers we are given:

$\pi \cdot 22 \cdot 6$ $\displaystyle \pi \cdot 22 \cdot 6$

Once we multiply these numbers, we get $24\pi$ $\displaystyle 24\pi$.

The unit for our answer is $in^{3}$ $\displaystyle in^{3}$ since we are solving a volume problem.

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Example Question #5 : Volume Of A Cylinder

Find the volume of a cylinder that has a radius of 2 inches and a height of 10 inches.

$V = \pi r^2 * h$ $\displaystyle V = \pi r^2 * h$

Possible Answers:

$40\pi \textup{ inches}^2$ $\displaystyle 40\pi \textup{ inches}^2$

$40\pi \textup{ inches}^3$ $\displaystyle 40\pi \textup{ inches}^3$

$10\pi \textup{ inches}^3$ $\displaystyle 10\pi \textup{ inches}^3$

$20\pi \textup{ inches}^3$ $\displaystyle 20\pi \textup{ inches}^3$

Correct answer:

$40\pi \textup{ inches}^3$ $\displaystyle 40\pi \textup{ inches}^3$

Explanation:

Radius = 2 Inches

Height = 10

$V = \prod r^2 * h$ $\displaystyle V = \prod r^2 * h$

$V = \prod * 2^2 * 10$ $\displaystyle V = \prod * 2^2 * 10$

$V = \prod * 40$ $\displaystyle V = \prod * 40$

$V = 40\pi Inches^3$ $\displaystyle V = 40\pi Inches^3$

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Example Question #2 : Volume Of A Cylinder

Find the volume of a cylinder with a diameter of 1 and a height of 2.

Possible Answers:

$2\pi$ $\displaystyle 2\pi$

$\frac{1}{8}\pi$ $\displaystyle \frac{1}{8}\pi$

$4\pi$ $\displaystyle 4\pi$

$\frac{1}{4}\pi$ $\displaystyle \frac{1}{4}\pi$

$\frac{1}{2}\pi$ $\displaystyle \frac{1}{2}\pi$

Correct answer:

$\frac{1}{2}\pi$ $\displaystyle \frac{1}{2}\pi$

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2h$ $\displaystyle V=\pi r^2h$

Find the radius by dividing the diameter by 2.

$r=\frac{d}{2} = \frac{1}{2}$ $\displaystyle r=\frac{d}{2} = \frac{1}{2}$

$V=\pi (\frac{1}{2})^2(2)=\pi(\frac{1}{4})(2) = \frac{1}{2}\pi$ $\displaystyle V=\pi (\frac{1}{2})^2(2)=\pi(\frac{1}{4})(2) = \frac{1}{2}\pi$

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Example Question #3 : Volume Of A Cylinder

The area of the circular base of a cylinder is $4\pi$ $\displaystyle 4\pi$. The height of the cylinder is $\displaystyle 4$. What is the volume of the cylinder?

Possible Answers:

$16\pi$ $\displaystyle 16\pi$

$4\pi +4$ $\displaystyle 4\pi +4$

$64\pi$ $\displaystyle 64\pi$

$32\pi$ $\displaystyle 32\pi$

$16\pi^2+4$ $\displaystyle 16\pi^2+4$

Correct answer:

$16\pi$ $\displaystyle 16\pi$

Explanation:

Write the formula to find the volume of the cylinder.

$V=\pi r^2 h$ $\displaystyle V=\pi r^2 h$

The $\pi r^2$ $\displaystyle \pi r^2$ term represents the area of the circular base. Multiply the given area and the height to obtain the area.

$V=(4\pi)(4) = 16\pi$ $\displaystyle V=(4\pi)(4) = 16\pi$

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Example Question #2 : Volume Of A Cylinder

Find the volume of a cylinder if the radius is 2 and the height is 12.

Possible Answers:

$15\pi$ $\displaystyle 15\pi$

$36\pi$ $\displaystyle 36\pi$

$24\pi$ $\displaystyle 24\pi$

$48\pi$ $\displaystyle 48\pi$

$12\pi$ $\displaystyle 12\pi$

Correct answer:

$48\pi$ $\displaystyle 48\pi$

Explanation:

Write the volume formula for a cylinder.

$V=\pi r^2h$ $\displaystyle V=\pi r^2h$

Substitute the dimensions.

$V=\pi (2)^2(12) = 48\pi$ $\displaystyle V=\pi (2)^2(12) = 48\pi$

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Example Question #1 : Volume Of A Cylinder

Find the volume of a cylinder with a radius and height of $2\pi$ $\displaystyle 2\pi$.

Possible Answers:

$4\pi^3$ $\displaystyle 4\pi^3$

$8\pi^3$ $\displaystyle 8\pi^3$

$8\pi^4$ $\displaystyle 8\pi^4$

$16\pi ^4$ $\displaystyle 16\pi ^4$

$4\pi^4$ $\displaystyle 4\pi^4$

Correct answer:

$8\pi^4$ $\displaystyle 8\pi^4$

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2h$ $\displaystyle V=\pi r^2h$

Substitute the dimensions.

$V=\pi (2\pi)^2(2\pi) = \pi(4\pi^2)(2\pi) = 8\pi^4$ $\displaystyle V=\pi (2\pi)^2(2\pi) = \pi(4\pi^2)(2\pi) = 8\pi^4$

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Example Question #1 : Volume Of A Cylinder

Find the volume of a cylinder with a base area of $\pi$ $\displaystyle \pi$ and a height of $\pi^2$ $\displaystyle \pi^2$.

Possible Answers:

$2\pi ^3$ $\displaystyle 2\pi ^3$

$\pi^4$ $\displaystyle \pi^4$

$\frac{\pi^4}{4}$ $\displaystyle \frac{\pi^4}{4}$

$\pi ^3$ $\displaystyle \pi ^3$

$3\pi ^3$ $\displaystyle 3\pi ^3$

Correct answer:

$\pi ^3$ $\displaystyle \pi ^3$

Explanation:

Write the formula to find the volume of the cylinder.

$V = \pi r^2 h = A_{\textup{circle}}h$ $\displaystyle V = \pi r^2 h = A_{\textup{circle}}h$

Because the base of the cylinder is a circle, the term $\pi r^2$ $\displaystyle \pi r^2$ represents the area of the circular base, which is already given.

Multiply the area with the height to obtain the volume.

$V= \pi (\pi^2)=\pi ^3$ $\displaystyle V= \pi (\pi^2)=\pi ^3$

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Pre-Algebra : Volume

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #1 : Volume Of A Cylinder

Example Question #2 : Volume Of A Cylinder

Example Question #1 : Volume Of A Cylinder

Example Question #1 : Volume Of A Cylinder

Example Question #5 : Volume Of A Cylinder

Example Question #2 : Volume Of A Cylinder

Example Question #3 : Volume Of A Cylinder

Example Question #2 : Volume Of A Cylinder

Example Question #1 : Volume Of A Cylinder

Example Question #1 : Volume Of A Cylinder

All Pre-Algebra Resources

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