Question

A circle with radius of \greenD{6\,\text{cm}}6cmstart color #1fab54, 6, start text, c, m, end text, end color #1fab54 sits inside a circle with radius of \blueD{9\,\text{cm}}9cmstart color #11accd, 9, 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

Answer: $141 cm^{2}$

Step-by-step explanation:

We have two circles:

Cirlce 1, with a radius $r=6 cm$ and area $A_{1}$:

$A_{1}=\pi r^{2}$

And Cicle 2, with a radius $R=9 cm$ and area $A_{2}$:

$A_{1}=\pi R^{2}$

Since Circle 1 is inside Circle 2 and assuming the area of the shaded region is the shown in the attached image, its area is:

$A=A_{2}-A_{1}=\pi R^{2}-\pi r^{2}$

$A=\pi (R^{2}- r^{2})$

$A=\pi ((9cm)^{2}- (6cm)^{2})$

Finally:

$A=141.37 cm^{2} \approx 141 cm^{2}$