What is the area of the gray region, in square units, if the radius of the larger circle is four times the radius of the smaller circle and the diameter of the smaller circle is 2 units? Express your answer in terms of pi.

Guest Apr 16, 2020

#1**0 **

This similar question will help you:

https://artofproblemsolving.com/wiki/index.php/2018_AMC_8_Problems/Problem_15

CalTheGreat Apr 16, 2020

#2**+2 **

Since the diameter of the smaller circle is 2 units the radius is 1 unit.

We know that the radius of the larger circle is 4 times the radius of the smaller circle the radius of the larger circle is 4 units.

Notice that the area of the gray region is equal to the larger circle minus the smaller one.

Since the area of a circle is \(\pi \cdot r^2\) we can find the area of the gray area by substituting.

\(\pi \cdot 4^2 - \pi \cdot 1^2 = 16\pi - \pi = 15\pi\).

HumanCalc Apr 16, 2020