High School Math : How to find the radius of a sphere

Study concepts, example questions & explanations for High School Math

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Example Questions

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

Find the radius of a sphere whose surface area is \displaystyle SA=100cm^{2}.

Possible Answers:

\displaystyle 8.22cm

\displaystyle 3.54cm

Not enough information to solve

\displaystyle 35.45cm

\displaystyle 2.82cm

Correct answer:

\displaystyle 2.82cm

Explanation:

We know that the surface area of the spere is \displaystyle SA=100cm^{2}.

\displaystyle SA=4\pi r^{2}

\displaystyle 100cm^{2}=4\pi r^{2}

Rearrange and solve for \displaystyle r.

\displaystyle r^{2}=\frac{100cm^{2}}{4\pi}

\displaystyle \dpi{100} r=\sqrt{\frac{100cm^{2}}{4\pi}}

\displaystyle \dpi{100}\rightarrow 2.82cm

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

What is the radius of a sphere that has a surface area of \displaystyle 16\pi?

Possible Answers:

\displaystyle \sqrt{2\pi }

\displaystyle 8\pi

\displaystyle 2

\displaystyle 2\sqrt{\pi }

\displaystyle 8\sqrt{\pi }

Correct answer:

\displaystyle 2

Explanation:

The standard equation to find the area of a sphere is \displaystyle SA=4\pi r^2 where \displaystyle r denotes the radius. Rearrange this equation in terms of \displaystyle r:

\displaystyle r=\sqrt{\frac{SA}{4\pi }}

To find the answer, substitute the given surface area into this equation and solve for the radius:

\displaystyle r=\sqrt{\frac{16\pi }{4\pi }}=\sqrt{4}=2

Example Question #3 : How To Find The Radius Of A Sphere

Given that the volume of a sphere is \displaystyle 12\pi, what is the radius?

Possible Answers:

\displaystyle 3

\displaystyle \sqrt[3]{9}

\displaystyle \sqrt[3]{12 }

\displaystyle 9\pi

\displaystyle \sqrt{9\pi }

Correct answer:

\displaystyle \sqrt[3]{9}

Explanation:

The standard equation to find the volume of a sphere is 

\displaystyle V=\frac{4}{3}\pi r^3 where \displaystyle r denotes the radius. Rearrange this equation in terms of \displaystyle r:

\displaystyle r=\sqrt[3]{\frac{3V}{4\pi }}

Substitute the given volume into this equation and solve for the radius:

\displaystyle r=\sqrt[3]{\frac{3V}{4\pi }}=\sqrt[3]{\frac{3\cdot 12\pi }{4\pi }}=\sqrt[3]{\frac{36\pi }{4\pi }}=\sqrt[3]{9 }

Example Question #4 : How To Find The Radius Of A Sphere

What is the radius of a sphere with a volume of \displaystyle 288\pi?

Possible Answers:

\displaystyle 36

\displaystyle 12

\displaystyle 6

\displaystyle 24

Correct answer:

\displaystyle 6

Explanation:

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

\displaystyle 288\pi=\frac{4}{3}\pi r^3

\displaystyle \frac{288\pi}{\pi}=\frac{4\pi r^3}{3\pi}

\displaystyle 288=\frac{4r^3}{3}

\displaystyle (288)(\frac{3}{4})=\frac{3}{4}(\frac{4r^3}{3})

\displaystyle 216=r^3

\displaystyle \sqrt[3]{216}=\sqrt[3]{r^3}

\displaystyle 6=r

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