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Pre-Algebra : Volume

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Example Questions

Example Question #2 : Volume Of A Sphere

A hollow sphere has a diameter of 8 inches from the center of the sphere to the outermost shell. The shell of the sphere is 1 inch thick. What is the volume of the shell or wall of the sphere?

Possible Answers:

V=268.1in^3

V=56in^3

V=179.6in^3

V=89 in^3

V=192.4in^3

Correct answer:

V=89 in^3

Explanation:

The questions asks the volume of the wall of the sphere only. Therefore it is necessary to find the total volume of the large sphere and subtract the volume of the inner sphere (formed by the wall) from it.

Volume of large sphere:

$V=\frac{4}{3} \pi r^3=\frac{4}{3}\pi(4^3)=268.1in^3$

Volume of inner sphere:

$V=\frac{4}{3} \pi r^3=\frac{4}{3}\pi(3.5^3)=179.6in^3$

The difference between the two volumes leaves only the volume of the wall of the sphere:

268.1-179.6=89in^3

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Example Question #4 : Volume Of A Sphere

Regulations for professional soccer state that the diameter of the ball must be 8.65 inches for a size 5 regulation ball. What is the volume of the soccer ball?

Possible Answers:

V=339in^2

V=339in^3

The answer is not present.

V=393in^3

V=933in^3

Correct answer:

V=339in^3

Explanation:

The volume of a sphere is given by $\frac{4}{3}\pi r^3$ . The problem listed the diameter of the ball. Half of this number is the radius.

$V=\frac{4}{3}\pi (4.325)^3=339in^3$

When using a calculator to solve these types of problems it is best to do the problem in chunks to avoid input errors. For instance find out what the value of the radius cubed is first. Then multiply the other terms.

The units of volume are always cubed, not squared.

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Example Question #6 : Volume Of A Sphere

Michelle plays softball for her high school. She is the only pitcher on the team. She is the only player that is guaranteed to touch the ball on every play. The problem is, her hands are not big enough to get a grip on the ball because the ball is too big. What is the volume of the softball that has a diameter of 6 inches?

Possible Answers:

$288\pi inches^3$

$36\pi inches^2$

$48\pi inches^3$

$288\pi inches^2$

$36 \pi inches^3$

Correct answer:

$36 \pi inches^3$

Explanation:

The formula to find the volume of a sphere is $\frac{4}{3} * \pi * r^3$

Find the radius of the softball and substitute that in place of r.

Answer will be left in pi format.

4/3 = 1.33333333

r^3 = 3^3

r^3 = 27

1.33333333 * 27 = 36

$36\pi inches^3$

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Example Question #3 : Volume Of A Sphere

Find the volume of a sphere with a diameter of .

Possible Answers:

$375\pi$

$\frac{500}{3}\pi$

$500\pi$

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

$\frac{400}{3}\pi$

Correct answer:

$\frac{500}{3}\pi$

Explanation:

Write the formula to find the volume of a sphere.

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

Divide the diameter by two to obtain the radius. The radius is five.

Substitute the radius into the volume equation.

$V=\frac{4}{3}\pi (5)^3=\frac{4}{3}\pi (125) = \frac{500}{3}\pi$

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Example Question #4 : Volume Of A Sphere

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

Possible Answers:

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

$\frac{7}{3}\pi$

$\frac{16}{3}\pi^4$

$\frac{16}{9}\pi^3$

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

Correct answer:

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

Explanation:

Write the formula for the volume of a sphere and substitute the radius.

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

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Example Question #11 : Volume Of A Sphere

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

Possible Answers:

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

$\frac{256}{81}\pi$

$\frac{64}{9}\pi$

$\frac{9}{128}\pi$

$9\pi$

Correct answer:

$\frac{9}{128}\pi$

Explanation:

Write the formula to find the volume of a sphere.

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

Divide the diameter by two, or multiply the diameter by one-half to obtain the radius.

$r=\frac{1}{2}d= \frac{1}{2} \times \frac{3}{4}= \frac{3}{8}$

$V=\frac{4}{3}\pi (\frac{3}{8})^3 = \frac{4}{3} \pi (\frac{27}{512}) = \frac{9}{128}\pi$

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Example Question #11 : Volume Of A Sphere

Find the volume of a sphere with a diameter of .

Possible Answers:

$9\pi$

$134\pi$

$144\pi$

$36\pi$

$288\pi$

Correct answer:

$36\pi$

Explanation:

Write the formula for the volume of a sphere.

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

The radius is half the diameter of , which is .

Substitute the radius.

$V=\frac{4}{3}\pi (3)^3 = \frac{4}{3}\pi (27)= 36\pi$

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Example Question #13 : Volume Of A Sphere

Find the volume of a sphere if the radius is 8.

Possible Answers:

$256\pi$

$2048\pi$

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

$64\pi$

$\frac{2048\pi}{3}$

Correct answer:

$\frac{2048\pi}{3}$

Explanation:

Write the formula for the volume of a sphere.

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

Substitute the radius.

$V=\frac{4}{3}\pi (8)^3$

$V= \frac{4}{3} \pi \cdot 8\cdot 8 \cdot 8$

Multiply the whole numbers with the numerator of the fraction. The denominator will remain the same.

$V= \frac{4}{3} \pi \cdot 8\cdot 8 \cdot 8= \frac{2048\pi}{3}$

The volume of the sphere is: $\frac{2048\pi}{3}$

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Example Question #14 : Volume Of A Sphere

Find the volume of a sphere with a radius of $7\pi$ .

Possible Answers:

$49\pi$

$\frac{1372\pi ^4}{3}$

$49\pi ^2$

$\frac{1372\pi ^3}{3}$

$418\pi ^4$

Correct answer:

$\frac{1372\pi ^4}{3}$

Explanation:

Write the formula for the volume of a sphere.

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

Substitute the radius into the equation.

$V_\textup{sphere} = \frac{4}{3}\pi (7\pi)^3$

Expand the terms of the equation.

$V_\textup{sphere} = \frac{4}{3}\pi (7\pi)(7\pi)(7\pi)$

Multiply the four along with the three sevens.

$V_\textup{sphere} = \frac{1372\pi ^4}{3}$

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Example Question #223 : Geometry

You have a balloon filled with water in the shape of a perfect sphere. The balloon has a diameter of 6cm. Find the volume of water inside the balloon.

Possible Answers:

$6\pi$

$9\pi$

$12\pi$

$15\pi$

$3\pi$

Correct answer:

$12\pi$

Explanation:

The formula to find the volume of a sphere is

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

where r is the radius of the sphere.

We know the diameter of the balloon is 6cm. The radius is half of the diameter, so the radius is 3cm. Now, we substitute.

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

$V = \frac{4}{3} \pi \cdot 9$

We can simplify by cancelling out the 3 and the 9. We get

$V = 4 \pi \cdot 3$

$V = 12\pi$

Therefore, the volume of the balloon is $12\pi$ .

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Pre-Algebra : Volume

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #2 : Volume Of A Sphere

Example Question #4 : Volume Of A Sphere

Example Question #6 : Volume Of A Sphere

Example Question #3 : Volume Of A Sphere

Example Question #4 : Volume Of A Sphere

Example Question #11 : Volume Of A Sphere

Example Question #11 : Volume Of A Sphere

Example Question #13 : Volume Of A Sphere

Example Question #14 : Volume Of A Sphere

Example Question #223 : Geometry

All Pre-Algebra Resources

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