If two circles have the same radius, is having the combined area of the two circles the same as having twice the circumference? This has been bothering me for the past hour and I cant seem to solve it. It would seem likely to be the same.

Answer 1

nope!

Area of circle with radius r = πr^2
so combined area of two of those circles = 2πr^2

twice the circumference = 2(2πr) = 4πr

e.g. suppose the radius = 5 cm
area of 2 such circles = 2(π(25)) = 50π

twice the circumference = 2(2π(5)) = 20π
clearly different!