Question

Find the area of the shaded sector. Leave your answer in terms of π.

24π ft2

18π ft2

32π ft2

3π ft2

Answer 1

18π ft2

Explanation:

The circle has a radius of 12 ft and the angle of the sector is 45°.

Area of the sector (A) is given by the formula below:

`A=(\theta)/(360)* \pi r^2`

Where
`\theta` is the angle of the sector and r is the radius of the circle

We know r = 12 and
`\theta` = 45°

Plugging these into the formula and simplifying, we get:

`A=(\theta)/(360)* \pi r^2\\A=(45)/(360)* \pi (12)^2\\A=(1)/(8)* \pi (144)\\A=18 \pi`

Thus, the area is
`18 \pi` sq. ft.

Answer 2

18π ft^2

Explanation:

The area of the circle is

pi *r^2

pi * 12^2

144pi

The part that is shaded is 45 degrees

An entire circle is 360 degrees

The fraction that is shaded is 45/360 = 1/8

Multiply the area by the fraction that is shaded

1/8 * 144 pi

18 pi