The volume of a right circular cylinder is the same numerical value as its total surface area. Find the smallest integral value for the radius of the cylinder. 1,2,3,4, or can’t be determined. Please explain!
pir2h = 2pir2 + 2pirh
rh = 2r + 2h
Does this help?
After obtaining rh = 2r + 2h, a nice solution is to bring everything to the LHS and add 4:
rh - 2r - 2h + 4 = 4
This factors to (r-2)(h-2) = 4. If r = 1, then we get h = -2 which is impossible. If r = 2, then r-2 = 0. The smallest integral value of r is 3, in which h=6.