Question

A circle with area 36 has a sector with a central angle of 11/6pi

radians.
What is the area of the sector?

Answer 1

33 sq. units

Explanation:

The area of a sector can be calculated using the formula;

`A = ( 1)/(2) {r}^(2) \theta`

From the given information, the area of the circle is 36 and the angle of sector is

This means

`\pi {r}^(2) = 36 \\ {r}^(2) = (36)/(\pi)`

We substitute the values into the formula to get:

`A = ( 1)/(2) * (36)/(\pi) * (11)/(6) \pi`

We cancel out common factors to get:

`A =33`

The area of sector is 33 square units