Question

the sum of areas of two circles is 80 square meters find the lencgh of radius of each circles if one of them is twice as larger than the other what is the radius of the largest circle

Answer 1

A1 + A2 = 80 ,,, R1= 2R2
pi* R1^2 + pi * R2^2 = 80
R1^2 + R2^2 = 80/pi
sub. by R1 = 2R2
(2R2)^2 + R2^2 = 80/pi
5R2^2 = 80/pi
R2^2 = 16/pi
R2 = 2.256 m
R1 = 2 R2
So,, R1 = 4.513 m

Answer 2

area of a cirlce=πr²
we have two radius:2r and r
area of the cirlce₁ + area of the circle₂=80 m²
area of the circle₁=π(2r)²
area of the circle₂=πr²
Then, we can suggest this quation:

π(2r)²+πr²=80

4πr²+πr²=80
π(4r²+r²)=80
π(5r²)=80
5πr²=80
r²=80/5π
r=√(80/5π)≈2.26

radius of the largest cirlce=2r=2(2.26)=4.51

Answer: the radius of the largest circle is 4.51 m