Question

Express answer in exact form.

Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius.


help me please ...?

Answer 1

Radii and chord form an equilateral triangle. The angle of the larger segment is
`360^o-60^o=300^o`.

The length of the larger segment is


`l= (2r\pi\alpha)/(360^o)= (2* 8\pi300^o)/(360^o)= ( 16\pi5)/(6)= ( 8\pi5)/(3)=( 40\pi)/(3)`