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GED Math : 3-Dimensional Geometry

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Example Questions

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Example Question #11 : Volume Of A Sphere

What is the volume of a sphere with a radius of $\frac{3}{2}\pi$ ?

Possible Answers:

$9\pi ^3$

$\frac{9}{2}\pi ^3$

$\frac{9}{4}\pi ^4$

$\frac{9}{2}\pi ^4$

$\frac{9}{8}\pi ^6$

Correct answer:

$\frac{9}{2}\pi ^4$

Explanation:

Write the formula for the volume of a sphere.

$V= \frac{4}{3} \pi r^3$

Substitute the radius into this equation.

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

The answer is: $\frac{9}{2}\pi ^4$

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Example Question #11 : Volume Of A Sphere

Determine the volume of a sphere in feet, if the diameter of the sphere is 6 inches.

Possible Answers:

$\frac{1}{24} \pi\textup{ ft}^3$

$288\pi \textup{ ft}^3$

$\frac{1}{96}\pi \textup{ ft}^3$

$\frac{1}{48}\pi \textup{ ft}^3$

$\frac{1}{124}\pi \textup{ ft}^3$

Correct answer:

$\frac{1}{48}\pi \textup{ ft}^3$

Explanation:

Write the formula for the volume of a sphere.

$V= \frac{4}{3}\pi r^3$

We will need to convert the diameter in terms of feet. There are 12 inches to a foot.

$6 \textup{ in} (\frac{1 \textup{ ft}}{12 \textup{ in}}) = \frac{1}{2} \textup{ ft}$

The radius is half the diameter. Multiply this value by one-half to obtain the radius.

$\frac{1}{2} \textup{ ft} \cdot \frac{1}{2} = \frac{1}{4} \textup{ ft}$

Substitute the radius in the formula.

$V= \frac{4}{3}\pi (\frac{1}{4} \textup{ ft})^3 = \frac{4}{3}\pi (\frac{1}{4} \textup{ ft})(\frac{1}{4} \textup{ ft})(\frac{1}{4} \textup{ ft})$

The answer is: $\frac{1}{48}\pi \textup{ ft}^3$

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Example Question #563 : Geometry And Graphs

Let $\pi = 3.14$ .

If a sphere has a radius of 3cm, find the volume.

Possible Answers:

$84.78\text{cm}^3$

$37.68\text{cm}^3$

$113.04\text{cm}^3$

$25.12\text{cm}^3$

$28.26\text{cm}^3$

Correct answer:

$113.04\text{cm}^3$

Explanation:

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

$V = \frac{4}{3} \cdot \pi \cdot r^3$

where r is the radius of the sphere.

Now, we know $\pi = 3.14$ . We know the radius of the sphere is 3cm. So, we can substitute. We get

$V = \frac{4}{3} \cdot 3.14 \cdot (3\text{cm})^3$

$V = \frac{4}{3} \cdot 3.14 \cdot 27\text{cm}^3$

$V = \frac{4}{3} \cdot 27\text{cm}^3 \cdot 3.14$

Now, the 3 and the 27 can both be divided by 3. So, we get

$V = \frac{4}{1} \cdot 9\text{cm}^3 \cdot 3.14$

$V = 4 \cdot 9\text{cm}^3 \cdot 3.14$

$V = 36\text{cm}^3 \cdot 3.14$

$V = 113.04\text{cm}^3$

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Example Question #11 : Volume Of A Sphere

Find the volume of a sphere with a radius of $\frac{3}{4}\pi$ .

Possible Answers:

$\pi^4$

$\frac{9}{16} \pi ^4$

$\frac{9}{4} \pi ^3$

$\pi ^3$

$\frac{9}{16}\pi$

Correct answer:

$\frac{9}{16} \pi ^4$

Explanation:

Write the formula for the volume of a sphere.

$V = \frac{4}{3}\pi r^3$

Substitute the radius into the equation.

$V = \frac{4}{3}\pi (\frac{3}{4}\pi)^3= \frac{4}{3}\pi (\frac{3}{4}\pi)(\frac{3}{4}\pi)(\frac{3}{4}\pi)$

The answer is: $\frac{9}{16} \pi ^4$

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Example Question #11 : 3 Dimensional Geometry

Determine the volume of a sphere with a radius of 6.

Possible Answers:

$144\pi$

$72\pi$

$288\pi$

$324\pi$

$48\pi$

Correct answer:

$288\pi$

Explanation:

Write the formula for the volume of a sphere.

$V= \frac{4}{3}\pi r^3$

Substitute the radius.

$V= \frac{4}{3}\pi (6)^3 = \frac{4}{3}\pi (6) (6) (6) = 288\pi$

The answer is: $288\pi$

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Example Question #11 : Volume Of A Sphere

Find the volume of a sphere with a radius of 6cm.

Possible Answers:

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

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

$648\pi \text{ cm}^3$

$864\pi \text{ cm}^3$

$216\pi \text{ cm}^3$

Correct answer:

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

Explanation:

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

$V = \frac{4}{3}\pi r^3$

where r is the radius of the sphere.

Now, we know the radius of the sphere is 6cm. So, we can substitute. We get

$V = \frac{4}{3} \cdot \pi \cdot (6\text{cm})^3$

$V = \frac{4}{3} \cdot \pi \cdot 216\text{cm}^3$

Now, the 3 and the 216 can both be divided by 3. So, we get

$V= \frac{4}{1} \cdot \pi \cdot 72\text{cm}^3$

$V= 4 \cdot \pi \cdot 72\text{cm}^3$

$V = 4 \cdot 72\text{cm}^3 \cdot \pi$

$V = 288\text{cm}^3 \cdot \pi$

$V = 288\pi \text{ cm}^3$

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Example Question #567 : Geometry And Graphs

Find the volume of a sphere with a surface area of $4\pi$ .

Possible Answers:

$\pi$

$\frac{1}{3}\pi$

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

$\frac{256}{3}\pi$

$\frac{4}{3} \pi$

Correct answer:

$\frac{4}{3} \pi$

Explanation:

Write the formulas for the surface area and volume of a sphere.

$A = 4\pi r^2$

$V=\frac{4}{3} \pi r^3$

Substitute the surface area into the first formula and solve for the radius.

$4\pi = 4\pi r^2$

Divide by $4\pi$ on both sides.

$\frac{4\pi }{4\pi}= \frac{4\pi r^2}{4\pi}$

1=r^2

Square root both sides.

r=1

Substitute the radius into the volume formula.

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

The answer is: $\frac{4}{3} \pi$

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Example Question #568 : Geometry And Graphs

Find the volume of a sphere with a radius of $\pi ^6$ .

Possible Answers:

$\frac{16}{3}\pi ^{19}$

$\frac{4}{3}\pi ^{10}$

$4\pi^{10}$

$\frac{16}{3}\pi ^{10}$

$\frac{4}{3}\pi ^{19}$

Correct answer:

$\frac{4}{3}\pi ^{19}$

Explanation:

Write the formula for the volume of a sphere.

$V=\frac{4}{3}\pi r^3$

Substitute the radius.

$V=\frac{4}{3}\pi (\pi ^6)^3= \frac{4}{3}\pi (\pi ^6) (\pi ^6) (\pi ^6)$

The answer is: $\frac{4}{3}\pi ^{19}$

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Example Question #571 : Geometry And Graphs

You are 3D printing a ball which will be an integral piece to the project you are creating. If you need the ball to have a radius of 12cm, what volume of material will be required?

Possible Answers:

2304 cm^3

$144\pi cm^3$

1728 cm^3

7234.56 cm^3

Correct answer:

7234.56 cm^3

Explanation:

You are 3D printing a ball which will be an integral piece to the project you are creating. If you need the ball to have a radius of 12cm, what volume of material will be required?

We are asked to find the volume of a sphere, to do so, we should use the formula for volume of a sphere.

$V_{sphere}=\frac{4}{3} \pi r^3$

So, let's plug in our radius and solve:

$V_{sphere}=\frac{4}{3} \pi (12cm)^3=\frac{4}{3} \pi 1728cm^3=7234.56 cm^3$

So our answer is:

7234.56 cm^3

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Example Question #12 : 3 Dimensional Geometry

You are given a spherical floating speaker for your birthday. If the speaker has a radius of 5 inches, what is its volume?

Possible Answers:

500in^3

523.56in^3

166.67in^3

125in^3

Correct answer:

523.56in^3

Explanation:

You are given a spherical floating speaker for your birthday. If the speaker has a radius of 5 inches, what is its volume?

We need to find the volume of a sphere. To do so, we need the following formula:

$V=\frac{4}{3}\pi r^3$

We know r is 5, so just plug and simplify

$V=\frac{4}{3}\pi (5in)^3\approx 523.56in^3$

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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 #11 : Volume Of A Sphere

Example Question #11 : Volume Of A Sphere

Example Question #563 : Geometry And Graphs

Example Question #11 : Volume Of A Sphere

Example Question #11 : 3 Dimensional Geometry

Example Question #11 : Volume Of A Sphere

Example Question #567 : Geometry And Graphs

Example Question #568 : Geometry And Graphs

Example Question #571 : Geometry And Graphs

Example Question #12 : 3 Dimensional Geometry

All GED Math Resources

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