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GED Math : GED Math

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

Example Questions

Example Question #561 : Geometry And Graphs

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

Possible Answers:

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

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

$\pi ^3$

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

$\pi^4$

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 #1531 : Ged Math

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

Possible Answers:

$48\pi$

$144\pi$

$324\pi$

$72\pi$

$288\pi$

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 #13 : Volume Of A Sphere

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

Possible Answers:

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

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

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

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

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

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 #16 : 3 Dimensional Geometry

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

Possible Answers:

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

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

$\pi$

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

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

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 #563 : Geometry And Graphs

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

Possible Answers:

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

$4\pi^{10}$

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

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

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

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:

7234.56 cm^3

1728 cm^3

2304 cm^3

$144\pi cm^3$

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 #1532 : Ged Math

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:

523.56in^3

125in^3

500in^3

166.67in^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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Example Question #572 : Geometry And Graphs

A sphere has surface area $20 \pi$ . Give its volume.

Possible Answers:

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

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

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

$\frac{20 \pi \sqrt{5}}{3}$

Correct answer:

$\frac{20 \pi \sqrt{5}}{3}$

Explanation:

The formula for the surface area of a sphere, given its radius , is

$A= 4 \pi r^{2}$ .

Set $A = 20 \pi$ and solve for to get the radius.

$4 \pi r^{2} = 20 \pi$

Divide both sides by $4 \pi$ :

$\frac{4 \pi r^{2}}{4 \pi} = \frac{20 \pi}{4 \pi}$

$r^{2} = 5$

Take the positive square root of both sides to obtain the radius:

$r = \sqrt{5}$

The formula for the volume of a sphere, given its radius , is

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

Substitute $\sqrt{5}$ for in this formula and evaluate the expression:

$V = \frac{4 \pi (\sqrt{5})^{3}}{3}$

$= \frac{4 \pi \cdot \sqrt{5}\cdot \sqrt{5} \cdot \sqrt{5}}{3}$

$= \frac{4 \pi \cdot5 \cdot \sqrt{5}}{3}$

$= \frac{20 \pi \sqrt{5}}{3}$

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Example Question #1533 : Ged Math

A ball in the shape of a sphere has a radius of inches. What volume of air, in cubic inches, is needed to fully inflate the ball?

Possible Answers:

2144.66

2811.24

1905.21

268.08

Correct answer:

2144.66

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume}=\frac{4}{3}\pi r^3$

Plug in the given radius to solve for the volume.

$\text{Volume}=\frac{4}{3}\pi (8^3)=\frac{2048\pi}{3}=2144.66$

Make sure to round to two places after the decimal point.

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Example Question #574 : Geometry And Graphs

A sphere has a radius of . Find its volume.

Possible Answers:

$45\Pi$

$36\Pi$

$50\Pi$

$60\Pi$

$18\Pi$

Correct answer:

$36\Pi$

Explanation:

The formula for the volume of a sphere is $(4/3)\Pi r^3$ , with standing for radius. Since you know that the radius of the sphere is , all you have to do is plug in for and solve. Once you do that you learn that the volume is $36\Pi$ .

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All GED Math Resources

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #561 : Geometry And Graphs

Example Question #1531 : Ged Math

Example Question #13 : Volume Of A Sphere

Example Question #16 : 3 Dimensional Geometry

Example Question #563 : Geometry And Graphs

Example Question #571 : Geometry And Graphs

Example Question #1532 : Ged Math

Example Question #572 : Geometry And Graphs

Example Question #1533 : Ged Math

Example Question #574 : Geometry And Graphs

All GED Math Resources

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