Which expression gives the surface area of a cylinder with radius r and height h?

Which expression gives the surface area of a cylinder with radius r and height h?

• A. π r^2 h
• B. 2π rh
• C. 2π r(r + h)
• D. π r^2

Answer: (C)

Surface area of a cylinder comes from combining the area of the curved side with the areas of the two circular ends. The curved side, when unrolled, is a rectangle with height h and width equal to the circumference 2πr, so its area is 2πrh. The two ends form circles, each with area πr^2, totaling 2πr^2. Adding them gives SA = 2πrh + 2πr^2 = 2πr(r + h). This matches the expression. The other options correspond to volume (πr^2h), the side area only (2πrh), or the area of a single circle (πr^2), none of which account for the full surface area.

Surface area of a cylinder comes from combining the area of the curved side with the areas of the two circular ends. The curved side, when unrolled, is a rectangle with height h and width equal to the circumference 2πr, so its area is 2πrh. The two ends form circles, each with area πr^2, totaling 2πr^2. Adding them gives SA = 2πrh + 2πr^2 = 2πr(r + h). This matches the expression. The other options correspond to volume (πr^2h), the side area only (2πrh), or the area of a single circle (πr^2), none of which account for the full surface area.