Which expression correctly represents the total surface area of a cylinder?

Which expression correctly represents the total surface area of a cylinder?

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

Answer: (D)

Total surface area of a cylinder combines the curved side with the two circular ends. The side area is the circumference of the base times the height: 2πr × h = 2πrh. Each base has area πr^2, and there are two bases, giving 2πr^2. Adding them together gives 2πrh + 2πr^2, which can be factored as 2πr(h + r). This matches the total surface area expression in terms of radius and height. The other forms represent only part of the surface (lateral side or the two bases) or, in the case of πd(h+r), would be equivalent only if you use diameter d with d = 2r. Since the problem uses radius and height, 2πr(h + r) is the appropriate form.

Total surface area of a cylinder combines the curved side with the two circular ends. The side area is the circumference of the base times the height: 2πr × h = 2πrh. Each base has area πr^2, and there are two bases, giving 2πr^2. Adding them together gives 2πrh + 2πr^2, which can be factored as 2πr(h + r). This matches the total surface area expression in terms of radius and height. The other forms represent only part of the surface (lateral side or the two bases) or, in the case of πd(h+r), would be equivalent only if you use diameter d with d = 2r. Since the problem uses radius and height, 2πr(h + r) is the appropriate form.