Question

Express answer in exact form.

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

$l= \frac{2r\pi\alpha}{360^o}= \frac{2\times 8\pi300^o}{360^o}= \frac{ 16\pi5}{6}= \frac{ 8\pi5}{3}=\frac{ 40\pi}{3}$