Question

The sum of the areas of two circles is 80pie square meters. Find the length of a radius of each circle if one of them is twice as long as the other. What is the radius of the larger circle?

Answer 1

Write an equation to model this situation.

A1+A2=80

The formula for the area of a circle is A=πr^2. Let A1 be πr^2. If A2's r is twice A1's, then A2=π(2r)^2:

πr^2+π(2r)^2=80

*Simplify*

πr^2+π4r^2=80

*Combine like terms*

5πr^2=80

*Divide both sides by 5π*

r^2=16/π

*Take the square root of both sides*

r=4/√π

*Multiply r by 2 for the second radius*

r2=8/√π

Hope this helps!!