The sum of two circles is 80 pi square meters. Find the length of the radius if one of them is twice as long as the other

Length of Radius of large circle= 8

Lenght radius of first circle= 2

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION

The sum of the areas of two circles is 80π square meters. Find the length of a radius of each circle if one of them is twice as long as the other.

What is the radius of the larger circle?

Area of a circle can be calculated by Below formula

A = πr^2eqn(1)

Let ( X) = area of first circle

Y= the area of second circle

Rx= radius of first circle

Ry = radius of second circle

From the question, we know that

[X+ Y] = 80π eqn(2)

Substitute the radius formula for the area,

[π(Rx)^2 + π (Ry)^2] = 80π eqn(3)

But from the question, Radius of second circle is twice of the second one, then

Ry = 2Rx eqn(4)

If we substitute eqn (4) into eqn(3)

[ π(Rx)^2 + π (2Rx)^2 = 80π

If factorize π out, then cancel it out

π[(Rx)^2 + π (2Rx)^2 = 80π

Then we have

(Rx)^2 + 4(Rx)^2 = 80

5(Rx)^2 = 80

(Rx)^2= 80/5

(Rx)^2= 16

(Rx)= 4

From eqn(4)

Ry = 2Rx

Ry= 2(4)

Ry= 8

Rx= 2 and Ry= 8

Hence, radius of first circle= 2

Lenght Radius of second circle= 8