Question

A circle has a sector with area $33\pi$ and central angle of $\frac{11}{6}\pi$ radius. What is the area of the circle? Either enter a exact answer in terms of $\pi$ or use $\pi =3.14$

Answer 1

Area of a sector $=\frac{radian}{2\pi }\times \left(\pi r^2\right)$

$\frac{\frac{11}{6}\pi }{2\pi }\times \pi r^2=33\pi$

$\pi r^2=$ area of circle (A)

$\frac{11}{12}\times A=33\pi$

$A=\frac{33\times 12}{11}\pi$

$A+36\pi$ unit square is area of circle.