Question

A circle with a radius of 3cm sits inside of a circle with a radius of 5cm. What is the area of the Shaded Region? Round your answer to the nearest hundereth

Answer 1

Answer:

$A=50.27\ cm^2$

Step-by-step explanation:

The complete question is

A circle with a radius of 3 cm sits inside of a circle with a radius of 5 cm. 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

The area of the shaded region is equal to subtract the area of the smaller circle from the area of the larger circle

Remember that

The area of the circle is equal to

$A=\pi r^{2}$

so

The area of the shaded region is

$A=\pi [r_1^2-r_2^2]$

where

$r_1=5\ cm$

$r_2=3\ cm$

substitute

$A=\pi [5^2-3^2]$

$A=\pi [16]$

$A=16\pi\ cm^2$

assume

$\pi =3.1416$

substitute

$A=16(3.1416)=50.27\ cm^2$