Question

The diameter of the larger circle is 12.5 cm. The diameter of the smaller circle is 8.5 cm.

What is the best approximation for the area of the shaded region?

Answer 1

The best approximation for the area of the shaded region is
`65.94\ cm^2`

Explanation:

The complete question is

The diameter of the larger circle is 12.5 cm. The diameter of the smaller circle is 8.5 cm.

What is the best approximation for the area of the shaded region?

Use 3.14 to approximate pi.

Small circle inside big circle, shaded region outside smaller circle and inside larger circle

we know that

To find out the area of the shaded region subtract the area of the smaller circle from the area of the larger circle

Remember that

The area of the circle is

`A=\pi r^(2)`

so

`A=\pi [r_1^(2)-r_2^(2)]`

where

r_1 is the radius of the larger circle

r_2 is the area of the smaller circle

we have

`r_1=12.5/2=6.25\ cm` ---> the radius is half the diameter

`r_2=8.5/2=4.25\ cm` ---> the radius is half the diameter

`\pi =3.14`

substitute

`A=3.14[6.25^(2)-4.25^(2)]`

`A=65.94\ cm^2`