Question

Please help find the central angle and perimeter !

Answer 1

Explanation:

We will have the following

*First: We have that the area of a sector of a circle is given by the expression:

A = r²a/2

Here r is the radius and alpha is the central angle.

*Second: We determine the central angle as follows:

`36\pi =`

(12)²a/2 ➡️ a = 36í•2/(12) ²➡️

`a = (1)/(2) \pi`

So, the central angle has a measurement of 1/2 pi.

Third: We determine the perimeter of the sector as follows:

First: we determine the arc length with two times the radius, that is:

p = 2(12) +

`6\pi`

➡️ p = 24 +

`6\pi`

So, the perimeter of the sector is 24+ 6pi meters [ Approximately 43 meters].