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weqwewe [10]
3 years ago
8

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?
Mathematics
1 answer:
Alborosie3 years ago
3 0

Answer:

r = 4m --- small circle

R =8m --- big circle

Step-by-step 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

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