The formula for the surface area of a sphere is: SA = 4πr^2

Question

What equation shows the formula in terms r?

Answer 1

To express the surface area of a sphere (SA) in terms of the radius \( r \), you can start with the original formula:

\[ SA = 4\pi r^2 \]

To solve for \( r \), follow these steps:

1. Divide both sides by \( 4\pi \):

\[ \frac{SA}{4\pi} = r^2 \]

2. Take the square root of both sides to solve for \( r \):

\[ r = \sqrt{\frac{SA}{4\pi}} \]

Thus, the equation that shows the formula for the radius \( r \) in terms of the surface area \( SA \) is:

\[ r = \sqrt{\frac{SA}{4\pi}} \]