Question

A circle with radius of 3 cm sits inside a circle with radius of 5 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth.

Answer 1

About 50.24 cm^2 (Area of Shaded Region)

Explanation:

Let's calculate the area of the shaded region by calculating the area of the bigger circle subtracted by the area of the smaller, nested circle:

The area of the bigger circle, given it's radius of 5 cm, can be calculated through the area formula πr^2. Now let's substitute, and, for simplicity, keep π as it is:

π (5 cm)^2 =

25π cm^2

Now the area of the smaller circle, given it's radius of 3 cm, can be calculated through the area formula πr^2 as done before. Again let us substitute, and, for simplicity, keep π as it is:

π (3 cm)^2 =

9π cm^2

To calculate the area of the shaded region, as discussed before, should be the difference between the larger and smaller circle's area as such:

25π cm^2 - 9πcm^2 =

16π cm^2

Now let's take π as 3.14 and calculate:

16(3.14) cm^2 =

Area of Shaded Region: 50.24 cm^2

Answer 2

Hello!!

So first you need to find the area of the green circle. The formula for finding area for a circle is A = π r2. So the area for the green circle is 28.26 cm. Then you need to find the area of the blue circle. (Using the same formula) which would be 78.5. Then you subtract the value of the green circle to get the value of the shaded region which then your final answer is 50.24 cm. Hope this helped!!