The height of a cylinder is three times the diameter of the base. The surface area of thre ylinder is 126pi ft^2. What is thr radius of the base?

The answer is 3 ft

The surface area (SA) of a cylinder with radius r and height h is:

SA = 2πr² + 2πrh = π (2r² + 2rh)

We have:

SA = 126π ft²

h = 3 * d

d = 2r

h = 3 * 2r = 6r

126π = π (2r² + 2rh)

126 = 2r² + 2rh

126 = 2r² + 2r * 6r

126 = 2r² + 12r²

126 = 14r²

r² = 126/14

r² = 9

r = √9

r = 3