Which of the following represents the surface area of a cylinder?

• A. πrh
• B. 4πr^2
• C. 2πrh + 2πr^2
• D. 2πr(h+r)

Answer: (C)

Think about a cylinder’s surface area as the sum of the curved side and the two circular ends. The curved side area comes from the circumference times height: 2πr times h, which is 2πrh. Each end has area πr^2, and two ends give 2πr^2. Add them together and you get 2πrh + 2πr^2, which can also be written by factoring as 2πr(h + r). This exactly represents the total surface area of the cylinder. The other forms don’t match for different reasons: πrh misses the two ends, 4πr^2 is the surface area of a sphere, and 2πr(h + r) is just another way to write the same total.