It is important to note that the longest diagonal of the cube is also the diameter of the sphere in which the cube is inscribed. First find the length of the longest diagonal of the cube (equal to the length of the diameter of the sphere), as shown below, using the Pythagorean Theorem:

Since the diameter’s length is 6, the radius’s length is 3. Plugging this value into the formula for the volume of a sphere, V=(4/3)πr³, we find that the volume is C)36π.