The height of a cylinder is three times the diameter of the base. the total surface area of the cylinder is 126pi ft^2. what is the radius of the base?

The easiest way to do this is to put the height in terms of radius. If diameter is 2 times the radius, then d = 2r. If the height is 3 times the diameter and diameter is twice the radius, then d = 2r, h = 3d, and 3d = 6r. Therefore, h = 6r by the transitive property of equality. Anyway ... The formula for surface area of a cylinder is SA = 2 pi r^2 + 2 pi r h. Let's sub in what we know now, which is that SA = 126 and h = 6r: 126 pi = 2 pi r^2 + 2 pi r (6r). Simplifying that we get

126 pi = 2 pi r^2 + 12 pi r^2. Simplifying even further gives us

126 pi = 14 pi r^2. Divide both sides by 14 pi to get 9 = r^2. Now take the square root of both sides to get that r = + / - 3. But since we know that radius cannot be negative, the answer is that the radius is 3.