Question

The area of the circle is 81 π units². It is divided into 6 equal parts. What is the perimeter of the shaded region in terms of π?

I attached a diagram as well.


I'd also appreciate anyone who can help me, as I am in need of it.

Thank you.

Answer 1

Area of a circle:
(pi)r^2
(pi)r^2 = (pi) 81
r^2 = 81
r = 9

Perimeter of a circle:
2(pi)r
[2(pi)9]:3 = (18pi):3 = 6pi [the two small arcs]

9 = 2.87pi

2.87pi x 4 = 11.5pi

Perimeter of shaded area:
11.5pi + 6pi = 17.5pi