What is the surface area formula for a cylinder including ends?

What is the surface area formula for a cylinder including ends?

• A. 2πr²
• B. 2πr² + 2πrh
• C. 2πrh
• D. 4πr^2

Answer: (B)

Think about what covers a cylinder with both ends. The two circular bases contribute 2πr^2, since each base has area πr^2. The curved side adds the side area, which is circumference times height: (2πr)·h = 2πrh. Add these together for the total surface area: 2πr^2 + 2πrh. This is the complete surface area. For contrast, options that include only 2πr^2 or only 2πrh omit either the ends or the side, and 4πr^2 doubles just the ends, not incorporating the height.

Think about what covers a cylinder with both ends. The two circular bases contribute 2πr^2, since each base has area πr^2. The curved side adds the side area, which is circumference times height: (2πr)·h = 2πrh. Add these together for the total surface area: 2πr^2 + 2πrh. This is the complete surface area. For contrast, options that include only 2πr^2 or only 2πrh omit either the ends or the side, and 4πr^2 doubles just the ends, not incorporating the height.