a cylinder has a radius of 15 ft and a height of 25 ft. what is the exact surface area of the cylinder

1200 ft²

Step-by-step explanation:

We assume that we want the total surface area, which includes the curving sides and the flat ends.

1. Curving sides: We are actually finding the area of a flat piece of material whose length is C = 2πr and whose width is the height of the cylinder, h. Then this side area is A = 2πrh. Here, that area is

A = 2π (15 ft) (25 ft) = 750π ft²

2. Ends: The end area is A = πr², and there are two ends.

The total area of the ends is A = 2πr², which here is A = 2π (15 ft) ², or

A = 450π ft².

Thus, the total exact surface area of this cylinder is

A = 450π ft² + 750π ft² = 1200 ft²