Question

A circle with the radius of 6 sits inside a circle of 9. What is the area of the shaded region?

Answer 1

Answer:

$141.37\text{ units}^2$.

Step-by-step explanation:

We have been given two concentric circles and we are asked to find the area of the shaded region.

The area of the shaded region will be equal to the area of bigger circle minus area of smaller circle.

$\text{Area of circle}=\pi r^2$

$\text{Area of shaded region}=\pi*9^2-\pi*6^2$

$\text{Area of shaded region}=\pi*81-\pi*36$

$\text{Area of shaded region}=45\pi$

$\text{Area of shaded region}=141.371669\approx 141.37$

Therefore, the area of the shaded region is 141.37 square units.

Answer 2

Equation for the area of a circle- π r² 
The 2 radiuses are 6 and 9. 
6 squared is 36 and 9 squared is 81. 
The smaller one is 36π and the larger one is 81π. 
The difference between them is the area of the shaded region. 
81π - 36π = 45π 
Use 3.14 for π. 
45 x 3.14 = 141.3 u² 
Hope this helps!