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Pre-Algebra : Volume of a Sphere

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Example Questions

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 of a Sphere

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

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

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