Joe has exactly enough paint to paint the surface of a cube whose main diagonal is 2. It turns out that this is also exactly enough paint to paint the surface of a sphere. Find the radius of the sphere.
+128408 If the main diagonal is 2......then we can find the side, s by
2 = sqrt ( 3s^2)
2 = sqrt (3) s
s = 2/sqrt (3)
s^2 = 4/3
Surface area of this cube is 6 s^2 = 6 (4/3) = 24/3 = 8 units^2
And for the sphere radius :
8 = 4 pi r^2
r^2 = 8 / ( 4 pi) = 2/ pi
r = sqrt (2/pi) units
