Question

The formula for the surface area of a sphere is SA = 4πr2
Which equation shows the formula in terms of r?

(1 point)
Responses

r = SA2π−−−√
r = SA2π−−−√

r = SA4π−−−√
r = SA4π−−−√

r = 2SA4π
r = 2SA4π

r = 4SAπ−−−√

Answer 1

To rewrite the formula for the surface area of a sphere, \( SA = 4\pi r^2 \), in terms of \( r \), we need to solve for \( r \).

1. Start with the original formula:
\[
SA = 4\pi r^2
\]

2. Divide both sides by \( 4\pi \):
\[
\frac{SA}{4\pi} = r^2
\]

3. Now take the square root of both sides to solve for \( r \):
\[
r = \sqrt{\frac{SA}{4\pi}}
\]

This can be simplified to:
\[
r = \frac{\sqrt{SA}}{\sqrt{4\pi}} = \frac{\sqrt{SA}}{2\sqrt{\pi}}
\]

However, based on the answers provided, the equivalent expression for \( r \) is:
\[
r = \sqrt{\frac{SA}{4\pi}} = \frac{1}{2} \sqrt{\frac{SA}{\pi}}
\]

Comparing with the options given, the correct answer is:
\[
r = \frac{SA}{4\pi} \text{ (r = SA4π−−−√)}
\]

The correct response is:
**r = SA/4π−−−√**