Question

In a circle, I 90° sector has an area of 36 pi inches squared what is the radius of the circle

Answer 1

im not sure but i think its 6. sorry if its wrong : (

Answer 2

Answer: 12 inches

Explanation:

Given: In a circle , the area of a sector =
`36 \pi\text{ inches}`

Measure of Arc
`\theta=90^(\circ)`

The formula to calculate the area of the sector is given by:-

`\text{ Area of sector}=(\theta)/(360^(\circ))*\pi r^2`

Substitute area and angle in the formula, we get

`36\pi=(90^(\circ))/(360^(\circ))*\pi r^2\\\\\Rightarrow36\pi=(1)/(4)*\pi r^2\\\\\Rightarrow\ r^2=36*4\\\\\Rightarrow r^2=144\\\\\Rightarrow\ r=12\ \text{ inches}`

Hence, the radius of the circle = 12 inches.