Question 618928
A sphere is circumscribed about an 8-inch by 8-inch by 8-inch cube. Find the volume of the sphere to the nearest cubic inch.
---------------
The diameter of the sphere = the cube's long diagonal between 2 vertices not on the same face.
{{{d = sqrt(8^2 + 8^2 + 8^2) = sqrt(192)}}}
{{{r = d/2 = sqrt(48)}}}
--------
For the sphere:
{{{Vol = 4*pi*r^3/3 = 4*pi*48*sqrt(48)/3 = 64*pi*sqrt(48)}}} cubic inches