Question

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

Answer 1

Answer:

$\sqrt{\frac{668}{\pi} }$ feet  given the area is 167 ft squared

Step-by-step 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

$\sqrt{\frac{668}{\pi} } =r$