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

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:

$R = 2r$

$R =2 * 4$

$R =8m$