Question

the equation for the area of a circle, a, is ( a = pi r^2 ) where r is the radius. which equation represents the radius in terms of the area?
( r = 2api )
( r = \frac{a}{2pi} )
( r = sqrt{api} )
( r = sqrt{\frac{a}{pi}} )

Explanation:

Step1: Start with the area formula

We have the formula for the area of a circle \( A = \pi r^2 \). Our goal is to solve for \( r \) in terms of \( A \).

Step2: Divide both sides by \( \pi \)

To isolate \( r^2 \), we divide both sides of the equation by \( \pi \). This gives us \( \frac{A}{\pi} = r^2 \).

Step3: Take the square root of both sides

Since \( r \) represents the radius (a non - negative quantity), we take the square root of both sides. Taking the square root of \( r^2 \) gives \( r \), and taking the square root of \( \frac{A}{\pi} \) gives \( \sqrt{\frac{A}{\pi}} \). So \( r=\sqrt{\frac{A}{\pi}} \).

Answer:

\( r = \sqrt{\frac{A}{\pi}} \) (corresponding to the option \( r=\sqrt{\frac{A}{\pi}} \))