Set up an equation and solve the problem. The sum of the areas of two circles is 160 $\pi$ square meters. Find the length of a radius of the smaller circle if one of them is 3 times as long as the other.
A) 16 meters
B) 3 meters
C) 5 meters
D) 4 meters
E) none of these

Question

Quizplus · Accepted Answer

Let the radius of the smaller circle be $ r $. Then the radius of the larger circle is $ 3r $. The area of the smaller circle is $ \pi r^2 $ and the area of the larger circle is $ \pi (3r)^2 = 9\pi r^2 $. The sum of the areas is $ \pi r^2 + 9\pi r^2 = 10\pi r^2 = 160\pi $. Solving for $ r $, we get $ 10r^2 = 160 $, so $ r^2 = 16 $, and $ r = 4 $ meters.

Set Up an Equation and Solve the Problem π\piπ Square Meters

Set Up an Equation and Solve the Problem $\pi$ Square Meters