It is known that a cube is inscribed in a sphere. If the volume of the cube is 30, what is the volume of the sphere?
Volume of a cube = lxlxl l^3 = 30 so the sides of the cube are = 3.10723 units
From the CENTER of the cube to one of its corners is the radius of the SPHERE
The Corner - to - corner diagonal thru-the-center distance of the cube is sqrt( l^2 + l^2 + l^2) = 5.3818 units
so the center to the corner is 1/2 of this or 2.6909 units = radius of SPHERE
VOLUME of SPHERE = 4/3 x pi x r^3
= 4/3 x pi x 2.6909^3 = 81.62 units^3