Question

A circle with radius of \greenD{4\,\text{cm}}4cmstart color #1fab54, 4, start text, c, m, end text, end color #1fab54 sits inside a circle with radius of \blueD{11\,\text{cm}}11cmstart color #11accd, 11, start text, c, m, end text, end color #11accd.

What is the area of the shaded region?
Round your final answer to the nearest hundredth

Answer 1

The area of the shaded region is
`329.87\ cm^2`

Explanation:

The correct question is

A circle with radius of 4cm sits inside a circle with a radius of 11cm. What is the area of the shaded region?

The shaded region is the area outside the smaller circle and inside the larger circle

we know that

To find out the shaded region subtract the area of the smaller circle from the area of the larger circle

so

`A=\pi r_a^(2) -\pi r_b^(2)`

simplify

`A=\pi (r_a^(2) -r_b^(2))`

where

r_a is the radius of the larger circle

r_b is the radius of the smaller circle

we have

`r_a=11\ cm\\r_b=4\ cm`

substitute

`A=\pi (11^(2) -4^(2))`

`A=\pi (105)\ cm^2`

assume

`\pi=3.1416`

substitute

`A=(3.1416)(105)=329.87\ cm^2`