Surface Area of a Cylinder: which expression represents SA of a cylinder with radius r and height h?

• A. πrh + πr^2
• B. 4πr^2
• C. 2πrh + 2πr^2
• D. 2πrh

Answer: (C)

The surface area of a cylinder is found by adding the area of the curved side to the areas of the two circular ends. The side forms a rectangle with height h and width equal to the circumference 2πr, so its area is 2πrh. Each end is a circle with area πr^2, and there are two ends, giving 2πr^2. Adding these pieces gives 2πrh + 2πr^2, which is the expression for the surface area. The other expressions miss a piece: one combines side area with only one base, another doubles the bases but ignores the side, and one has only the side.