Which expression correctly gives the surface area of a right circular cylinder in terms of its radius r and height h?

• A. 4 pi r^2
• B. pi r^2 + 2 pi r h
• C. 2 pi r^2 + 2 pi r h
• D. 2 pi r^2

Answer: (C)

The surface area of a right circular cylinder comes from two parts: the two circular bases and the curved side. Each base has area pi r^2, and with two bases that’s 2 pi r^2. The curved side can be thought of as a rectangle whose width is the base’s circumference, 2 pi r, and height is h, giving lateral area 2 pi r h. Add them together: 2 pi r^2 + 2 pi r h. This is why the correct expression is 2 pi r^2 + 2 pi r h. The other options miss either the lateral area or one of the bases, or miscount the components.