find radius in sector of a circle when theta=1/3 radian and A= 2 square feet.

Answer 1

The area of a sector can be given as A_s = θ / 2π A_c where A_c is the area of a whole circle = πr².

Substituting πr² into As = θ / 2π x πr².

As A_s = 2 ft² = 1/3 x 1/2 x r² Note that π cancel out. Solve for r² than take the square root. Also realize that the radius of a sector is the same as the radius of a whole circle.

r² = 2 ft² x 3 x 2 = 12 ft² and r = 3.46 ft