A circle with area 36 pi has a sector with a central angle of 11/6 pi radians what is the area of the cector

The area of the sector is 33.

Explanation:

A sector is a part of a circle that is formed by two radii (which forms a central angle), and an arc. The area of a sector (in radians) is given by:

                          = (θ ÷ ) ×

where: θ is the central angle of the sector and r is the radius of the circle of which the sector is a part.

Area of a circle = . But the area of the circles was given to be 36.

Area of the sector = (θ ÷ ) × area of the circle

                              = (θ ÷ ) ×36

θ has been given to be .

Therefore;

   Area of the sector = ( ÷ ) ×36

                                   = × 36

                                   = 11 × 3

                                   = 33

The area of the sector is 33.