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The surface area of a sphere is \(400 \pi in^2\). What is the sphere’s diameter, in inches?

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Question:

A
20

explanation

Using the formula for the surface area of a sphere from the formula sheet (and omitting the units), solve \(4 \pi r^2=400 \pi\) for r

\(\frac{\mathrm{4 \pi r^2} }{\mathrm{4 \pi }} = \frac{\mathrm{400 \pi } }{\mathrm{4 \pi }}\)

\(r^2=100\)

\(r= \sqrt{100} = 10\)

The diameter is twice the length of r, so the sphere’s diameter is 20 inches. (–10 is also a solution, but it is rejected because r cannot be negative.)

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