Question

Both circles have the same center. The circumference of the inner circle is 77.872 centimeters. What is the area of the shaded region?

Answer 1

Answer:

The area of the shaded region is $875.68\ cm^{2}$

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the large circle minus the area of the inner circle

step 1

Find the radius of the inner circle

we know that

The circumference is equal to

$C=2\pi r$

we have

$C=77.872\ cm$

substitute and solve for r

$77.872=2(3.14)r$

$r=77.872/[2(3.14)]=12.4\ cm$

step 2

Find the radius of the large circle

$r=12.4+8.4=20.8\ cm$

step 3

Find the area of the shaded region

$A=(3.14)[20.8^{2} -12.4^{2}]= 875.68\ cm^{2}$