Given:
Radius of small circle = 4 in.
Width of gray border = 2 in.
To find:
The area of the gray border.
Solution:
We have, radius of small circle:
[tex]r=4\text{ in.}[/tex]
The width of gray border is 2 in. So,t he radius of the larger circle is:
[tex]R=4+2\text{ in.}[/tex]
[tex]R=6\text{ in.}[/tex]
Now, area of gray border is the difference for area of larger circle and smaller circle.
[tex]A=\pi R^2-\pi r^2[/tex]
[tex]A=\pi (R^2-r^2)[/tex]
Substituting [tex]r=4,\ R=6[/tex] in the above formula, we get
[tex]A=\pi (6^2-4^2)[/tex]
[tex]A=\pi (36-16)[/tex]
[tex]A=\pi (20)[/tex]
[tex]A=20\pi[/tex]
The area of the gray border is [tex]20\pi [/tex] square inches. Therefore, the correct option is D.
