Which expression represents the lateral surface area of a cylinder using diameter d and height h?

Which expression represents the lateral surface area of a cylinder using diameter d and height h?

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

Answer: (A)

Lateral surface area of a cylinder is found by taking the distance around the sides (the circumference) and multiplying by the height. The circumference can be written in terms of diameter as πd (since d = 2r and C = 2πr). Multiply by the height h to get πdh. This is the expression that uses diameter and height, so it’s the correct form. The other expressions don’t fit as neatly: one uses the radius, not the specified diameter; converting r to d/2 would give πdh anyway, but the problem asks for a form in terms of d. The remaining option πd^2 resembles an area of a circle in terms of diameter but is actually four times the circle’s area in terms of diameter, so it does not represent the lateral surface area.

Lateral surface area of a cylinder is found by taking the distance around the sides (the circumference) and multiplying by the height. The circumference can be written in terms of diameter as πd (since d = 2r and C = 2πr). Multiply by the height h to get πdh. This is the expression that uses diameter and height, so it’s the correct form.

The other expressions don’t fit as neatly: one uses the radius, not the specified diameter; converting r to d/2 would give πdh anyway, but the problem asks for a form in terms of d. The remaining option πd^2 resembles an area of a circle in terms of diameter but is actually four times the circle’s area in terms of diameter, so it does not represent the lateral surface area.