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GED Math : 3-Dimensional Geometry

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #4 : Volume Of Other Solids

A cone has a diameter of 8in and a height of 9in. Find the volume.

Possible Answers:

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

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

$36\pi \text{ in}^3$

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

$45\pi \text{ in}^3$

Correct answer:

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

Explanation:

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

$V = \pi r^2 \frac{h}{3}$

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

Now, we know the diameter of the cone is 8in. We also know the diameter is two times the radius. Therefore, the radius is 4in.

We know the height of the cone is 9in.

Knowing all of this, we can substitute into the formula. We get

$V = \pi \cdot (4\text{in})^2 \cdot \frac{9\text{in}}{3}$

$V = \pi \cdot 16\text{in}^2 \cdot 3\text{in}$

$V = \pi \cdot 48\text{in}^3$

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

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Example Question #3 : Volume Of Other Solids

Find the volume of a cube with a height of 7in.

Possible Answers:

$294\text{in}^3$

$196\text{in}^3$

$216\text{in}^3$

$343\text{in}^3$

$245\text{in}^3$

Correct answer:

$343\text{in}^3$

Explanation:

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

$V = l \cdot w \cdot h$

where l is the length, w is the width, and h is the height of the cube.

Now, we know the height of the cube is 7in. Because it is a cube, all sides are equal. Therefore, the width and the length are also 7in. So, we can substitute. We get

$V = 7\text{in} \cdot 7\text{in} \cdot 7\text{in}$

$V = 49\text{in}^2 \cdot 7\text{in}$

$V = 343\text{in}^3$

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Example Question #1 : Volume Of Other Solids

Let $\pi = 3.14$ .

A cone has a height of 5in and a diameter of 12in. Find the volume.

Possible Answers:

$452.16\text{in}^3$

$188.4\text{in}^3$

$376.80\text{in}^3$

$471\text{in}^3$

$94.20\text{in}^3$

Correct answer:

$188.4\text{in}^3$

Explanation:

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

$V = \pi r^2 \frac{h}{3}$

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

We know $\pi=3.14$ .

We know the diameter of the cone is 12in. We know the diameter is two times the radius. So, the radius is 6in.

We know the height is 5in.

Now, we can substitute. We get

$V = 3.14 \cdot (6\text{in})^2 \cdot \frac{5\text{in}}{3}$

$V = 3.14 \cdot 36\text{in}^2 \cdot \frac{5\text{in}}{3}$

Now, we can simplify to make things easier. The 36 and the 3 can both be divided by 3. So, we get

$V = 3.14 \cdot 12\text{in}^2 \cdot \frac{5\text{in}}{1}$

$V = 3.14 \cdot 12\text{in}^2 \cdot 5\text{in}$

$V = 3.14 \cdot 60\text{in}^3$

$V = 188.4\text{in}^3$

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Example Question #2 : Volume Of Other Solids

If a cube has a width of 7in, find the volume.

Possible Answers:

$294\text{in}^3$

$49\text{in}^3$

$153.86\text{in}^3$

$216\text{in}^3$

$343\text{in}^3$

Correct answer:

$343\text{in}^3$

Explanation:

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

$V = l \cdot w \cdot h$

where l is the length, w is the width, and h is the height of the cube.

We know the width of the cube is 7in. Because it is a cube, all sides/lengths are equal. Therefore, the length and the height are also 7in.

Now, we can substitute. We get

$V = 7\text{in} \cdot 7\text{in} \cdot 7\text{in}$

$V = 7\text{in} \cdot 49\text{in}^2$

$V = 343\text{in}^3$

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Example Question #1631 : Ged Math

If a cube has a height of 8cm, find the volume.

Possible Answers:

$628\text{cm}^3$

$364\text{cm}^3$

$512\text{cm}^3$

$729\text{cm}^3$

$384\text{cm}^3$

Correct answer:

$512\text{cm}^3$

Explanation:

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

$V = l \cdot w \cdot h$

where l is the length, w is the width, and h is the height of the cube.

Now, we know the height of the cube is 8cm. Because it is a cube, all sides/lengths are the same. Therefore, the length and the width are also 8cm. So, we can substitute. We get

$V = 8\text{cm} \cdot 8\text{cm} \cdot 8\text{cm}$

$V = 64\text{cm}^2 \cdot 8\text{cm}$

$V = 512\text{cm}^3$

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Example Question #111 : 3 Dimensional Geometry

Let $\pi = 3.14$ .

Find the volume of a cone with the following measurements:

radius: 7cm
height: 9cm

Possible Answers:

$461.58\text{cm}^3$

$197.82\text{cm}^3$

$254.34\text{cm}^3$

$65.94\text{cm}^3$

$153.86\text{cm}^3$

Correct answer:

$461.58\text{cm}^3$

Explanation:

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

$V = \pi r^2 \frac{h}{3}$

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

Now, we know $\pi = 3.14$ . We know the radius of the cone is 7cm. We know the height of the cone is 9cm. So, we substitute. We get

$V = 3.14 \cdot (7\text{cm})^2 \cdot \frac{9\text{cm}}{3}$

$V = 3.14 \cdot 49\text{cm}^2 \cdot \frac{9\text{cm}}{3}$

$V = 3.14 \cdot 49\text{cm}^2 \cdot 3\text{cm}$

$V = 3.14 \cdot 147\text{cm}^3$

$V = 461.58\text{cm}^3$

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Example Question #112 : 3 Dimensional Geometry

Find the volume of a cube with a width of 11in.

Possible Answers:

$1221\text{in}^3$

$1111\text{in}^3$

$1212\text{in}^3$

$1121\text{in}^3$

$1331\text{in}^3$

Correct answer:

$1331\text{in}^3$

Explanation:

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

$V = l \cdot w \cdot h$

where l is the length, w is the width, and h is the height of the cube.

Now, we know the width of the cube is 11in. Because it is a cube, all widths/lengths/etc are the same. Therefore, the length and the height are also 11in. So, we substitute. We get

$V = 11\text{in} \cdot 11\text{in} \cdot 11\text{in}$

$V = 121\text{in}^2 \cdot 11\text{in}$

$V = 1331\text{in}^3$

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Example Question #11 : Volume Of Other Solids

Find the volume of a cone with a radius of 2 and a height of 10.

Possible Answers:

$\frac{40}{3}\pi$

$\frac{20}{3}\pi$

$20\pi$

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

$\frac{100}{3}\pi$

Correct answer:

$\frac{40}{3}\pi$

Explanation:

Write the formula for the volume of a cone.

$V =\frac{1}{3}\pi r^2 h$

Substitute the radius and height.

$V =\frac{1}{3}\pi (2)^2 (10) = \frac{40}{3}\pi$

The answer is: $\frac{40}{3}\pi$

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Example Question #671 : Geometry And Graphs

Find the volume of a cone with a radius of $6\pi$ and a height of .

Possible Answers:

$12\pi^2$

$24 \pi ^2$

$48 \pi ^3$

$24 \pi ^3$

$48 \pi ^4$

Correct answer:

$24 \pi ^3$

Explanation:

Write the formula for the volume of a cone.

$V = \frac{1}{3}\pi r^2h$

Substitute the radius and height into the formula.

$V = \frac{1}{3}\pi (6\pi)^2(2) = \frac{1}{3}\pi (6\pi)(6\pi)(2)$

The answer is: $24 \pi ^3$

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Example Question #672 : Geometry And Graphs

What is the volume of a hemisphere with a radius of 2?

Possible Answers:

$8\pi$

$\frac{8}{3}\pi$

$\frac{16}{3}\pi$

$\frac{32}{9}\pi$

$\frac{32}{3}\pi$

Correct answer:

$\frac{16}{3}\pi$

Explanation:

Recall that the volume of a full sphere is: $V= \frac{4}{3} \pi r^3$

A hemisphere would be half this volume.

$\frac{1}{2}(\frac{4}{3} \pi r^3) = \frac{2}{3} \pi r^3$

Substitute the radius.

$\frac{2}{3} \pi (2)^3 = \frac{2}{3} \pi (8) = \frac{16}{3}\pi$

The answer is: $\frac{16}{3}\pi$

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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 #4 : Volume Of Other Solids

Example Question #3 : Volume Of Other Solids

Example Question #1 : Volume Of Other Solids

Example Question #2 : Volume Of Other Solids

Example Question #1631 : Ged Math

Example Question #111 : 3 Dimensional Geometry

Example Question #112 : 3 Dimensional Geometry

Example Question #11 : Volume Of Other Solids

Example Question #671 : Geometry And Graphs

Example Question #672 : Geometry And Graphs

All GED Math Resources

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