Two circles have circumferences that add up to 18 π centimeters and areas that add up to 41π square centimeters. Find the radius of each circle.

Answer 1

2*pi * R1 + 2 * pi * r2 = 18*pi

2*pi ( r1 + r2) = 18*pi

r1 + r2 = 9

r2 = 9 - r1

pi * r1^2 + pi * r2^2 = 41 * pi

r1^2 + r2^2 = 41

r1^2 + (9 - r1)^2 = 41

Let r1 = R, so we can replace r1 with R

R^2 + 81 - 18R + R^2 = 41

2R^2 - 18R + 40 = 0

R^2 - 9R + 20 = 0

(R - 5)(R-4) = 0

So R=r1 = 5 and R = r1 = 4

if r1 = 5 then r2 = 9 - r1 = 9 - 5 = 4

If r1=4 then r2 = 9 - r1 = 9 - 4 = 5

So the radii is 5 and 4.

check:

pi*10 + pi*8 = 18*pi is the total circumference

pi*25 + pi*16 = 41*pi is the total area