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GED Math : Volume of a Cylinder

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Example Questions

Example Question #21 : Volume Of A Cylinder

A cylinder has the following measurements:

Height: 8in
Diameter: 6in

Find the volume.

Possible Answers:

$48\pi \text{ in}^3$

$64\pi \text{ in}^3$

$16\pi \text{ in}^3$

$72\pi \text{ in}^3$

$24\pi \text{ in}^3$

Correct answer:

$72\pi \text{ in}^3$

Explanation:

To find the volume of a cylinder, we will use the following formula:

$V = \pi r^2 h$

where r is the radius and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 6in. We know the diameter is two times the radius. Therefore, the radius is 3in.

We know the height of the cylinder is 8in.

Knowing this, we can substitute. We get

$V = \pi \cdot (3\text{in})^2 \cdot 8\text{in}$

$V = \pi \cdot 9\text{in}^2 \cdot 8\text{in}$

$V = \pi \cdot 72\text{in}^3$

$V = 72\pi \text{ in}^3$

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Example Question #615 : Geometry And Graphs

What is the volume of a cylinder with a base area of $\sqrt\pi$ and a height of ?

Possible Answers:

$9\pi$

$3\sqrt{\pi}$

$3\pi$

$9\sqrt{\pi}$

Correct answer:

$3\sqrt{\pi}$

Explanation:

Write the formula for the volume of the cylinder.

$V=\pi r^2h$

The base area is a circle, which is $\pi r^2$ , and the area is already given.

This means we can substitute the area into the formula as is.

$V=\sqrt{\pi}(3)$

The answer is: $3\sqrt{\pi}$

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Example Question #63 : 3 Dimensional Geometry

Find the volume of a cylinder with a base diameter of 6, and a height of 7.

Possible Answers:

$63\pi$

$21\pi$

$126\pi$

$42\pi$

$84\pi$

Correct answer:

$63\pi$

Explanation:

Write the formula for the area of a cylinder.

$V=\pi r^2 h$

The radius is half the diameter, of three.

Substitute the known dimensions into the formula.

$V=\pi (3)^2 7 = \pi (9) 7 = 63\pi$

The answer is: $63\pi$

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Example Question #62 : 3 Dimensional Geometry

Find the volume of a cylinder with a radius of 8, and a height of 20.

Possible Answers:

$640\pi$

$1280\pi$

$320\pi$

$120\pi$

$\frac{1280}{3}\pi$

Correct answer:

$1280\pi$

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2h$

Substitute the radius and height into the equation.

$V=\pi( 8)^2(20)= \pi( 64)(20)$

The answer is: $1280\pi$

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Example Question #71 : 3 Dimensional Geometry

Let $\pi = 3.14$

If a cylinder has a height of 7in and a radius of 4in, find the volume.

Possible Answers:

$175.84\text{in}^3$

$351.68\text{in}^3$

$615.44\text{in}^3$

$703.36\text{in}^3$

$87.92\text{in}^3$

Correct answer:

$351.68\text{in}^3$

Explanation:

To find the volume of a cylinder, we will use the following formula:

$V = \pi r^2 h$

where r is the radius and h is the height of the cylinder.

We know $\pi=3.14$ .

We know the radius of the cylinder is 4in.

We know the height of the cylinder is 7in.

Now, we can substitute. We get

$V = 3.14 \cdot (4\text{in})^2 \cdot 7\text{in}$

$V = 3.14 \cdot 16\text{in}^2 \cdot 7\text{in}$

$V = 3.14 \cdot 112\text{in}^3$

$V = 351.68\text{in}^3$

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Example Question #72 : 3 Dimensional Geometry

Find the volume of a cylinder with a base area of 15, and a height of 10.

Possible Answers:

$\frac{75}{4}\pi$

$2250\pi$

150

2250

$150\pi$

Correct answer:

150

Explanation:

Write the volume formula for the cylinder. The area of the base is a circle or $\pi r^2$ .

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

Substitute the base and height.

V =(15)(10) = 150

The volume is: 150

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Example Question #73 : 3 Dimensional Geometry

Let $\pi = 3.14$ .

Find the volume of a cylinder with a radius of 4cm and a height of 6cm.

Possible Answers:

$87.92\text{cm}^3$

$75.36\text{cm}^3$

$150.72\text{cm}^3$

$301.44\text{cm}^3$

$452.16\text{cm}^3$

Correct answer:

$301.44\text{cm}^3$

Explanation:

To find the volume of a cylinder, we will use the following formula:

$V = \pi r^2 h$

where r is the radius and h is the height of the cylinder.

Now, we know $\pi = 3.14$ . We know the radius of the cylinder is 4cm. We know the height of the cylinder is 6cm. So, we substitute. We get

$V = 3.14 \cdot (4\text{cm})^2 \cdot 6\text{cm}$

$V = 3.14 \cdot 16\text{cm}^2 \cdot 6\text{cm}$

$V = 3.14 \cdot 96\text{cm}^3$

$V = 301.44\text{cm}^3$

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Example Question #71 : 3 Dimensional Geometry

Find the volume of a cylinder with a radius of 10, and a height of 20.

Possible Answers:

$\frac{2000\pi}{3}$

$2000\pi$

$\frac{200\pi}{3}$

$4000\pi$

$200\pi$

Correct answer:

$2000\pi$

Explanation:

Write the formula for the volume of a cylinder.

$V= \pi r^2 h$

Substitute the radius and height.

$V= \pi (10)^2 (20) = \pi (100) (20)$

The answer is: $2000\pi$

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Example Question #72 : 3 Dimensional Geometry

Find the volume of a cylinder with a radius of 5 and a height of 12.

Possible Answers:

$120\pi$

$60\pi$

$90\pi$

$400\pi$

$300 \pi$

Correct answer:

$300 \pi$

Explanation:

Write the formula for the volume of a cylinder.

$V= \pi r^2 h$

Substitute the dimensions.

$V= \pi (5)^2 (12) = \pi (25) (12 )= 300 \pi$

The answer is: $300 \pi$

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Example Question #76 : 3 Dimensional Geometry

Determine the volume of a cylinder with a radius of $3\pi^4$ and a height of $\pi$ .

Possible Answers:

$3\pi ^{10}$

$3\pi ^{20}$

$9\pi ^6$

$9\pi ^{20}$

$9\pi ^{10}$

Correct answer:

$9\pi ^{10}$

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2 h$

Substitute the radius and height.

$V=\pi (3\pi^4)^2 (\pi)$

Simplify the terms.

$V=\pi (3\pi^4)^2 (\pi) = \pi (3\pi^4)(3\pi^4) (\pi)$

The answer is: $9\pi ^{10}$

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GED Math : Volume of a Cylinder

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #21 : Volume Of A Cylinder

Example Question #615 : Geometry And Graphs

Example Question #63 : 3 Dimensional Geometry

Example Question #62 : 3 Dimensional Geometry

Example Question #71 : 3 Dimensional Geometry

Example Question #72 : 3 Dimensional Geometry

Example Question #73 : 3 Dimensional Geometry

Example Question #71 : 3 Dimensional Geometry

Example Question #72 : 3 Dimensional Geometry

Example Question #76 : 3 Dimensional Geometry

All GED Math Resources

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