What is the formula for the surface area of an enclosed cylinder in terms of radius r, diameter d, and height h?

• A. 2πr^2 + πdh
• B. 2πr^2 + 2πrh
• C. πd^2 + 2πrh
• D. 2πrh + πd^2

Answer: (A)

Think of the cylinder’s surface area as the sum of the areas of the two bases and the curved side. The two circular bases give 2πr^2. The curved side, when unrolled, is a rectangle with width equal to the base circumference 2πr and height h, giving 2πrh. Since diameter d equals 2r, the lateral part 2πrh can be written as πdh. Put together, the total surface area is 2πr^2 + πdh. This matches the given option. The other forms either miss a base area or use diameter in a way that doesn’t reflect the correct base area or lateral area.