Question

What is the area of this shaded region?

Answer 1

`Area\ of\ a\ circle:\ A_O=\pi r^2\\\\larger\ circle:\\R=3+(4:2)=3+2=5\ (in)\\\\A_1=\pi\cdot5^2=25\pi\ (in^2)\\\\smaller\ circle:\\r=4:2=2\ (in)\\\\A_2=\pi\cdot2^2=4\pi\ (in^2)\\\\The\ area\ of\ shaded\ region:\\\\A=A_1-A_2\\\\A=25\pi-4\pi=21\pi\ (in^2)\\\\Answer:\boxed{A.\ 21\pi\ in^2}`

Answer 2

21π in²

A is correct

Explanation:

In the given figure, two concentric circle form.

Diameter of inner circle = 4 in

Thickness between the circle 3 in

Diameter of outer circle = 4 + 3 + 3 = 10 in

Radius is half of diameter of circle.

Outer circle radius, R = 5 in

Inner circle radius, r = 2 in

Formula:

Area of circle
`=\pi r^2`

Area of shaded region = Area of outer circle - Area of inner circle

`=\pi R^2-\pi r^2`

`=\pi(5^2-2^2)`

`=\pi(25-4)`

`=21\pi\text{ in}^2`

Hence, The area of shaded region is 21π in²