Question

The shaded region below is called an annulus sector. Calculate the area (in square feet) of the shaded region if the inner circle has radius 7 ft and the outer circle has radius 14 ft. Round your answer to the nearest square foot.

Answer 1

462 ft²

Explanation:

The area of the annulus sector is given by the area of the outer circle (radius of 14 ft) minus the area of the inner circle (radius of 7 ft).

The area of a circle is:

`A=\pi r^2`

Therefore, the area of the annulus sector is:

`A_A=A_O-A_I\\A_A=\pi*14^2-(\pi*7^2)\\A_A=147\pi\\A_A= 462\ ft^2`

The area, rounded to the nearest square foot, is 462 ft².