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ValentinkaMS [17]
3 years ago
11

How do I solve this problem?

Mathematics
1 answer:
Inessa05 [86]3 years ago
7 0

Answer:

\large\boxed{8\ m}

Step-by-step 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=\sqrt{16}\\\\r=4\ m\\\\The \radius\ of\ the\ larger\ circle:\\\\2r=2(4m)=8m

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