Question

#4: solve
the area a of a sector of a circle with radius r and angle-measure s (in degrees) is given by
( a = \frac{pi r^2 s}{360} ), solve for the radius r.

Explanation:

Step1: Start with the formula

The formula for the area \( A \) of a sector is \( A = \frac{\pi r^2 S}{360} \).

Step2: Multiply both sides by 360

To eliminate the denominator, multiply both sides by 360: \( 360A = \pi r^2 S \).

Step3: Divide both sides by \( \pi S \)

We get \( \frac{360A}{\pi S} = r^2 \).

Step4: Take the square root

Take the square root of both sides to solve for \( r \): \( r = \sqrt{\frac{360A}{\pi S}} \) (we consider the positive root since radius is positive).

Answer:

\( r = \sqrt{\frac{360A}{\pi S}} \)