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

Step-by-step 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:-

$\text{ Area of sector}=\frac{\theta}{360^{\circ}}\times\pi r^2$

Substitute area and angle in the formula, we get

$36\pi=\frac{90^{\circ}}{360^{\circ}}\times\pi r^2\\\\\Rightarrow36\pi=\frac{1}{4}\times\pi r^2\\\\\Rightarrow\ r^2=36\times4\\\\\Rightarrow r^2=144\\\\\Rightarrow\ r=12\ \text{ inches}$

Hence, the radius of the circle = 12 inches.