Question

A circle has an area of 36π in2. What is the area of a sector of the circle that has a central angle of

π 6?

A)3 in2
B)6 in2
C)12 in2
D)196 in2

Answer 1

Answer: Option 'A' is correct.

Explanation:

Since we have given that

Area of a circle = 36π in²

As we know the formula for "Area of circle ":

`Area=\pi r^2\\\\36\pi=\pi r^2`

Now, we need to calculate the area of sector.

As we know the formula for "Area of sector":

`Area\ of\ sector=(\theta)/(360\textdegree)\pi r^2\\\\Area\ of\ sector=(30)/(360)* 36\pi \\\\Area\ of\ sector=(1)/(12)* 36\pi\\\\Area\ of\ sector=3\pi\ in^2`

Hence, Option 'A' is correct.

Answer 2

A central angle : π / 6 = 30 °
30 ° = 360 ° / 12
The area of the sector is 1/12 of the area of a circle.
Therefore area of the sector is:
A = 36 π / 12 = 3 π
Answer: A ) 3 π in²