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Pre-Algebra : Volume of a Cylinder

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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:

$\small 80\pi$

$\small 20\pi$

$\small 40\pi$

$\small 80$

$\small 100\pi$

Correct answer:

$\small 80\pi$

Explanation:

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

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

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

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

$\small V = 80\pi$

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

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Example Question #1 : Volume Of A Cylinder

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

Possible Answers:

$\small 4000\pi$

$\small 2000$

$\small 500\pi$

$\small \small 2000\pi$

$\small 500$

Correct answer:

$\small \small 2000\pi$

Explanation:

The volume of a cylinder is given by the formula:

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

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

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

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

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Example Question #1 : Volume Of A Cylinder

What is the volume of a cylinder with a diameter equal to and height equal to ?

Possible Answers:

$144\pi$

$36\pi$

$72\pi$

$288\pi$

Correct answer:

$72\pi$

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:

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

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Example Question #4 : 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 $6\:in$ . The radius of the can is $2\:in$ . What is the volume of the can?

Possible Answers:

$6\pi\:in^3$

$12\pi\:in^3$

$22\pi\:in^3$

$72\pi\:in^3$

$24\pi\:in^3$

Correct answer:

$24\pi\:in^3$

Explanation:

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

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

Plug in the numbers we are given:

$\pi \cdot 22 \cdot 6$

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

The unit for our answer is $in^{3}$ 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.

$V = \pi r^2 * h$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Radius = 2 Inches

Height = 10

$V = \prod r^2 * h$

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

$V = \prod * 40$

$V = 40\pi Inches^3$

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Example Question #6 : Volume Of A Cylinder

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

Possible Answers:

$2\pi$

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

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

$4\pi$

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

Correct answer:

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

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2h$

Find the radius by dividing the diameter by 2.

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

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

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Example Question #231 : Geometry

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

Possible Answers:

$32\pi$

$4\pi +4$

$16\pi^2+4$

$16\pi$

$64\pi$

Correct answer:

$16\pi$

Explanation:

Write the formula to find the volume of the cylinder.

$V=\pi r^2 h$

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

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

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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:

$12\pi$

$36\pi$

$15\pi$

$48\pi$

$24\pi$

Correct answer:

$48\pi$

Explanation:

Write the volume formula for a cylinder.

$V=\pi r^2h$

Substitute the dimensions.

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

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Example Question #2 : Volume Of A Cylinder

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

Possible Answers:

$8\pi^4$

$16\pi ^4$

$8\pi^3$

$4\pi^4$

$4\pi^3$

Correct answer:

$8\pi^4$

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2h$

Substitute the dimensions.

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

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Example Question #10 : Volume Of A Cylinder

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

Possible Answers:

$2\pi ^3$

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

$3\pi ^3$

$\pi^4$

$\pi ^3$

Correct answer:

$\pi ^3$

Explanation:

Write the formula to find the volume of the cylinder.

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

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

Multiply the area with the height to obtain the volume.

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

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Pre-Algebra : Volume of a Cylinder

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #1 : Volume Of A Cylinder

Example Question #1 : Volume Of A Cylinder

Example Question #1 : Volume Of A Cylinder

Example Question #4 : Volume Of A Cylinder

Example Question #5 : Volume Of A Cylinder

Example Question #6 : Volume Of A Cylinder

Example Question #231 : Geometry

Example Question #2 : Volume Of A Cylinder

Example Question #2 : Volume Of A Cylinder

Example Question #10 : Volume Of A Cylinder

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