The figure below shows a round plate that is white with a 2-inch gray border around it What is the area of just the gray border?

Question

asked Aug 4, 2022 76.2k views

1 Answer

Mark Skelton · Answer 1 · 2022-08-10T07:02:31+0000

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:

$r=4\text{ in.}$

The width of gray border is 2 in. So,t he radius of the larger circle is:

$R=4+2\text{ in.}$

$R=6\text{ in.}$

Now, area of gray border is the difference for area of larger circle and smaller circle.

$A=\pi R^2-\pi r^2$

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

Substituting
$r=4,\ R=6$ in the above formula, we get

$A=\pi (6^2-4^2)$

$A=\pi (36-16)$

$A=\pi (20)$

$A=20\pi$

The area of the gray border is
$20\pi$ square inches. Therefore, the correct option is D.