Question

A cylinder is 6 cms in diameter and 6 cms in height. If spheres of the same size are made from the material obtained, what is the diameter of each sphere?

Answer 1

volume of the cylinder = πR² h = π (6/2)² 6 =54 π cm³
radius of spheres = R cm
volume of a sphere = 4π/3 R³  cm³

number of spheres = n = 54 π /(4π R³/3) = 81/(2 R³)
For R = 3 cm, we have    n = 3/2    not possible.
 for  R = 1 cm,  we get   n = 81/2  not possible.
For  R = 1/2 cm,  then  n = 81 * 4 = 324 

so the radius of the spheres is  1/2 cm or 1/4 cm or 1/8 cm  for  n to be an integer.