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GED Math : Volume of Other Solids

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Example Question #1631 : Ged Math

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

Possible Answers:

$364\text{cm}^3$

$729\text{cm}^3$

$628\text{cm}^3$

$512\text{cm}^3$

$384\text{cm}^3$

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 #662 : Geometry And Graphs

Let $\pi = 3.14$ .

Find the volume of a cone with the following measurements:

radius: 7cm
height: 9cm

Possible Answers:

$65.94\text{cm}^3$

$254.34\text{cm}^3$

$461.58\text{cm}^3$

$197.82\text{cm}^3$

$153.86\text{cm}^3$

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 #661 : Geometry And Graphs

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

Possible Answers:

$1331\text{in}^3$

$1121\text{in}^3$

$1111\text{in}^3$

$1221\text{in}^3$

$1212\text{in}^3$

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 #1632 : Ged Math

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

Possible Answers:

$24 \pi ^2$

$48 \pi ^3$

$48 \pi ^4$

$24 \pi ^3$

$12\pi^2$

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 #11 : Volume Of Other Solids

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

Possible Answers:

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

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

$8\pi$

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

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

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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Example Question #11 : Volume Of Other Solids

A cube has a length of 9cm. Find the volume.

Possible Answers:

$729\text{cm}^3$

$81\text{cm}^3$

$486\text{cm}^3$

$381\text{cm}^3$

$567\text{cm}^3$

Correct answer:

$729\text{cm}^3$

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 length of the cube is 9cm. Because it is a cube, all sides/lengths are equal. Therefore, the width and height are also 9cm.

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

$V = 9\text{cm} \cdot 9\text{cm} \cdot 9\text{cm}$

$V = 81\text{cm}^2 \cdot 9\text{cm}$

$V = 729\text{cm}^3$

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Example Question #11 : Volume Of Other Solids

Find the volume of a cube with a height of 6cm.

Possible Answers:

$36\text{cm}^3$

$216\text{cm}^3$

$252\text{cm}^3$

$180\text{cm}^3$

$27\text{cm}^3$

Correct answer:

$216\text{cm}^3$

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 6cm. Because it is a cube, all lengths/sides/etc are equal. Therefore, the length and the width are also 6cm.

So, we substitute. We get

$V = 6\text{cm} \cdot 6\text{cm} \cdot 6\text{cm}$

$V = 36\text{cm}^2 \cdot 6\text{cm}$

$V = 216\text{cm}^3$

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Example Question #675 : Geometry And Graphs

Find the volume of a cone with a radius of 8in and a height of 6in.

Possible Answers:

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

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

$128\pi \text{ in}^3$

$144\pi \text{ in}^3$

$384\pi \text{ in}^3$

Correct answer:

$128\pi \text{ in}^3$

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 radius is 8in. We know the height is 6in. So, we can substitute. We get

$V = \pi \cdot (8\text{in})^2 \cdot \frac{6\text{in}}{3}$

$V = \pi \cdot 64\text{in}^2 \cdot 2\text{in}$

$V = \pi \cdot 128\text{in}^3$

$V = 128\pi \text{ in}^3$

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Example Question #13 : Volume Of Other Solids

An office uses cone-shaped paper cups for water in their water cooler. The cups have a radius of inches and a height of 4.25 inches. If the water cooler can hold 1155 cubic inches of water, how many complete cups of water can the water cooler fill?

Possible Answers:

Correct answer:

Explanation:

Start by finding the volume of a cup.

Recall how to find the volume of a cone:

$\text{Volume of Cone}=\frac{1}{3}\pi r^2 h$

Plug in the given radius and height to find the volume.

$\text{Volume}=\frac{1}{3}\pi(3)^2(4.25)=40.055$

Now divide the total volume of the water in the water cooler by the volume of one cup in order to find how many complete cups the water cooler can fill.

$\text{Number of cups filled}=\frac{1155}{40.055}=28.84$

Since the question asks for the number of complete cups that can be filled, we must round down to .

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GED Math : Volume of Other Solids

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1631 : Ged Math

Example Question #662 : Geometry And Graphs

Example Question #661 : Geometry And Graphs

Example Question #11 : Volume Of Other Solids

Example Question #1632 : Ged Math

Example Question #11 : Volume Of Other Solids

Example Question #11 : Volume Of Other Solids

Example Question #11 : Volume Of Other Solids

Example Question #675 : Geometry And Graphs

Example Question #13 : Volume Of Other Solids

All GED Math Resources

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