Question

A circle with area 36π has a sector with a central angle of 11/6π radians. What is the area of the sector?

Answer 1

33pi or 103.62 squre units

Explanation:

`central \: angle \: ( \theta) \\ = (11)/(6) {\pi}^(c) = (11)/(6) * 180 \degree = 330 \degree \\ \\ area \: of \: sector \\ = ( \theta)/(360 \degree) * area \: of \: circle \\ \\ = ( 330 \degree)/(360 \degree) * 36 \: \pi \\ \\ = ( 330 )/(10 ) \pi \\ \\ = \red{ \bold{33\pi}} \: {units}^(2) \\ = 33 * 3.14 \\ = 103.62 \: {units}^(2) \\`