Question

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?

Answer 1

`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`