Either increasing the radius or the height of a cylinder by six inches will result in the same volume. The original height of the cylinder is two inches. What is the original radius in inches?
I need to find the original radius of the cylinder, which I will call r. I also need to know the formula for the volume of a cylinder, which is V = pi * r^2 * h, where h is the height. Further simplifying, I get 2r^2 + 24r + 72 = 8r^2. Subtracting 2r^2 from both sides, I get 6r^2 - 24r - 72 = 0. The solutions are r = 6 and r = -2, but I can ignore the negative one since it does not make sense for a radius. Therefore, the original radius is 6 inches. 