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

Question

asked May 13, 2021 125k views

2 Answers

Mamata Hegde · Answer 1 · 2021-05-19T11:35:23+0000

Answer:

The area of the sector is 33
$\pi$ .

Step-by-step 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 ÷
$2\pi$ ) ×
$\pi r^(2)$

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 =
$\pi r^(2)$ . But the area of the circles was given to be 36
$\pi$ .

Area of the sector = (θ ÷
$2\pi$ ) × area of the circle

= (θ ÷
$2\pi$ ) ×36
$\pi$

θ has been given to be
(11)/(6)
$\pi$ .

Therefore;

Area of the sector = (
(11)/(6)
$\pi$ ÷
$2\pi$ ) ×36
$\pi$

=
(11)/(12) × 36
$\pi$

= 11 × 3
$\pi$

= 33
$\pi$

The area of the sector is 33
$\pi$ .