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.

You need to divide 210 square inches by 35 inches and that’s going to give you 6 inches and that’s the length of the hypothenuse of the right triangle i hope that this you : )