Express answer in exact form.

Question

Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius. (Hint: A chord divides a circle into two segments. In problem 1, you found the area of the smaller segment.)

I've no idea how to do this, please help me out if you could!

Answer 1

If you did problem 1, then just subtract that from the area of the whole circle.

If not, let's do it now. Recall that the area of the smaller segment is

a = 1/2 r^2 (θ-sinθ)

So, what's θ? Draw your diagram, and you can easily see that

sin(θ/2) = 4/8 = 1/2
θ = π/3

Plug that into the formula, and you will have the area of the smaller segment.

Answer 2

Given a circle with an 8" radius, find the area of the smaller segment whose chord is 8" long