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GED Math : 3-Dimensional Geometry

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Example Questions

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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Example Question #77 : 3 Dimensional Geometry

Determine the volume of a cylinder with a base area of 8, and a height of 6.

Possible Answers:

384

$\textup{The answer is not given.}$

$48\pi$

$384\pi$

Correct answer:

Explanation:

Write the volume for a cylinder.

$V =\pi r^2h$

The base of a cylinder is a circle, and the area of the base is: $\pi r^2$

We can substitute the area and the height.

$V =\pi r^2h= Bh = 8(6) = 48$

The answer is:

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Example Question #78 : 3 Dimensional Geometry

Find the volume of a cylinder with a radius of 7in and a height of 4in.

Possible Answers:

$224\pi \text{ in}^3$

$112\pi \text{ in}^3$

$196\pi \text{ in}^3$

$448\pi \text{ in}^3$

$192\pi \text{ in}^3$

Correct answer:

$196\pi \text{ in}^3$

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 radius is 7in. We know the height is 4in. So, we substitute. We get

$V = \pi \cdot (7\text{in})^2 \cdot 3\text{in}$

$V = \pi \cdot 49\text{in}^2 \cdot 4\text{in}$

$V = \pi \cdot 196\text{in}^3$

$V = 196\pi \text{ in}^3$

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Example Question #73 : 3 Dimensional Geometry

Determine the volume of a cylinder with a radius of 3 and a height of 9.

Possible Answers:

$\frac{27}{2}\pi$

$27\pi$

$54\pi$

$243\pi$

$81\pi$

Correct answer:

$81\pi$

Explanation:

Write the formula for the volume of the cylinder.

$V=\pi r^2 h$

$V=\pi (3)^2 (9) = 81 \pi$

The answer is: $81\pi$

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Example Question #632 : Geometry And Graphs

Find the volume of a cylinder with a diameter of 6in and a height of 8in.

Possible Answers:

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

$96\pi \text{ in}^3$

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

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

$288\pi \text{ in}^3$

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. So, 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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GED Math : 3-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

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

Example Question #77 : 3 Dimensional Geometry

Example Question #78 : 3 Dimensional Geometry

Example Question #73 : 3 Dimensional Geometry

Example Question #632 : Geometry And Graphs

All GED Math Resources

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