Answer:
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^2............eqn(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
