Hi,
This problem does not involve as much math as you may think. Call the volume of the original cylinder V1 and the volume of the new cylinder V2. The generic volume equation for a cylinder is given as V = πr2 h where π or pi, is a constant, r is the radius of the top or bottom of the cylinder and h is the height of the cylinder. So comparing V2 to V1 gives you a constant, k, or the increase in size of V2 compared to V1. V2/V1 = k = π(2r)2 h/ π(r)2 h. π, r2 and h are the same values for each cylinder so they cancel each other out and that leaves you with k = 22/1 or k = 4. The new cylinder will have a volume that is 4 times larger than the original cylinder.