Question

How do I solve this problem?

Answer 1

`\large\boxed{8\ m}`

Explanation:

`\text{The formula of an area of a circle:}\\\\A_O=\pi r^2\\\\r-radius\\\\\text{We have the radius 2r and the radius r. Substitute:}\\\\Larger\ circle:\\\\A_L=\pi(2r)^2=\pi(2r)(2r)=4\pi r^2\\\\Smaller\ circle:\\\\A_S=\pi r^2`

`\text{We have the sum of the areas of the circles}\ A=80\pi\ m^2.\\\\A=A_L+A_S\\\\\text{Substitute:}\\\\4\pi r^2+\pi r^2=80\pi\\\\5\pi r^2=80\pi\qquad\text{divide both sides by}\ 5\pi\\\\r^2=16\to r=√(16)\\\\r=4\ m\\\\The \radius\ of\ the\ larger\ circle:\\\\2r=2(4m)=8m`