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

User Aqm
by
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1 Answer

6 votes

Answer:


r = 4m --- small circle


R =8m --- big circle

Explanation:

Given


Area = 80\pi\ m^2 -- sum of areas


R = 2r

Required

The radius of the larger circle

Area is calculated as;


Area = \pi r^2

For the smaller circle, we have:


A_1 = \pi r^2

For the big, we have


A_2 = \pi R^2

The sum of both is:


Area = A_1 + A_2


Area = \pi r^2 + \pi R^2

Substitute:
R = 2r


Area = \pi r^2 + \pi (2r)^2


Area = \pi r^2 + \pi *4r^2

Substitute
Area = 80\pi\ m^2


80\pi = \pi r^2 + \pi *4r^2

Factorize


80\pi = \pi[ r^2 + 4r^2]


80\pi = \pi[ 5r^2]

Divide both sides by
\pi


80 = 5r^2

Divide both sides by 5


16 = r^2

Take square roots of both sides


4 = r


r = 4m

The radius of the larger circle is:


R = 2r


R =2 * 4


R =8m

User Frnsys
by
3.9k points