Please help find the central angle and perimeter !

Question

asked Feb 23, 2022 136k views

1 Answer

Vin Shahrdar · Answer 1 · 2022-02-27T02:23:45+0000

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].