Question

In a circle, a 90° sector has area 167 ft2. What is the radius of the circle?

Answer 1

`\sqrt{(668)/(\pi) }` feet given the area is 167 ft squared

Explanation:

Since our sector as a central angle of 90 degree then it is only a 4th of the whole circle. The area of a circle is pi*r^2. We will only be using a 4th of that since are sector is only a 4th of the circle.

So the formula will be using for the area of our sector is A=1/4 *pi*r^2.

We are given the area is 167 so replace A with 167.

167=1/4 * pi *r^2

Multiply both sides by 4.

167*4 =pi * r^2

668=pi * r^2

Divide both sides by pi

668/pi =r^2

Square root both sides

`\sqrt{(668)/(\pi) } =r`