GRE Math : How to find the radius of a sphere

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Example Question #1 : How To Find The Radius Of A Sphere

If a sphere has a volume of 268.08 $\displaystyle 268.08$ cubic inches, what is the approximate radius of the sphere?

Possible Answers:

5.9 in $\displaystyle 5.9 in$

8 in $\displaystyle 8 in$

64 in $\displaystyle 64 in$

4.5 in $\displaystyle 4.5 in$

4 in $\displaystyle 4 in$

Correct answer:

4 in $\displaystyle 4 in$

Explanation:

The formula for the volume of a sphere is

$v=\frac{4}{3}(\pi r^3)$ $\displaystyle v=\frac{4}{3}(\pi r^3)$ where $\displaystyle r$ is the radius of the sphere.

Therefore,

$r=\sqrt[3]{\frac{3v}{(4\pi)}}$ $\displaystyle r=\sqrt[3]{\frac{3v}{(4\pi)}}$

$r=\sqrt[3]{\frac{3(268.08)}{(4\pi)}}=\sqrt[3]{63.999}=3.999$ $\displaystyle r=\sqrt[3]{\frac{3(268.08)}{(4\pi)}}=\sqrt[3]{63.999}=3.999$, giving us $r\approx4$ $\displaystyle r\approx4$.

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Example Question #1541 : Gre Quantitative Reasoning

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ $\displaystyle 9\textup{ x }6\textup{ x }12$. What is the volume of the largest possible sphere that could fit within this solid?

Possible Answers:

$288\pi$ $\displaystyle 288\pi$

$2304\pi$ $\displaystyle 2304\pi$

$36\pi$ $\displaystyle 36\pi$

$972\pi$ $\displaystyle 972\pi$

Correct answer:

$36\pi$ $\displaystyle 36\pi$

Explanation:

For a sphere to fit into the rectangular prism, its dimensions are constrained by the prism's smallest side, which forms its diameter. Therefore, the largest sphere will have a diameter of $\displaystyle 6$, and a radius of $\displaystyle 3$.

The volume of a sphere is given as:

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

And thus the volume of the largest possible sphere to fit into this prism is

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

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Example Question #2 : How To Find The Radius Of A Sphere

What is the radius of a sphere with volume $36\pi$ $\displaystyle 36\pi$ cubed units?

Possible Answers:

$\displaystyle 4$

$\displaystyle 6$

$\displaystyle 7$

$\displaystyle 2$

$\displaystyle 3$

Correct answer:

$\displaystyle 3$

Explanation:

The volume of a sphere is represented by the equation $\frac{4}{3}\pi r^3$ $\displaystyle \frac{4}{3}\pi r^3$. Set this equation equal to the volume given and solve for r:

$36\pi=\frac{4}{3}\pi r^3$ $\displaystyle 36\pi=\frac{4}{3}\pi r^3$

$36\pi\cdot \frac{3}{4}=\pi r^3$ $\displaystyle 36\pi\cdot \frac{3}{4}=\pi r^3$

$27\pi=\pi r^3$ $\displaystyle 27\pi=\pi r^3$

27=r^3 $\displaystyle 27=r^3$

r=3 $\displaystyle r=3$

Therefore, the radius of the sphere is 3.

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GRE Math : How to find the radius of a sphere

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Find The Radius Of A Sphere

Example Question #1541 : Gre Quantitative Reasoning

Example Question #2 : How To Find The Radius Of A Sphere

All GRE Math Resources

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