Question

In a circle, a 90° sector has area 36π ft2. What is the radius of the circle?. A. 18 ft. B. 16 ft. C. 6 ft. D. 12 ft

Answer 1

The area of the whole circle is four times the area of the given sector:

`Area\ of\ circle=36\pi* 4=\pi r^(2)`

`r^(2)=(36\pi* 4)/(\pi)=144`

`r= √(144) =12\ ft`

Answer 2

The area of the sector is the product of the area of the whole circle and the ratio of the angle over that of the whole circle, it is mathematically expressed as,
πr² x (90/360) = 36π ft²
Solving for r in the equation gives an answer of 12 ft. Therefore, the answer is letter D. 12 ft.