Which formula gives the lateral surface area of a right circular cylinder (not including the top and bottom)?

Which formula gives the lateral surface area of a right circular cylinder (not including the top and bottom)?

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

Answer: (A)

Think of the side of a cylinder as a curved surface. If you unwrap that curved surface, it becomes a rectangle. The height of that rectangle is the cylinder’s height, h, and the width is the circumference of the base, which is 2πr. The area of that rectangle is width times height, so the lateral surface area is (2πr) × h = 2πrh. πr^2 is the area of a circle (the base), not the side. πd^2 would be π(2r)^2 = 4πr^2, which isn’t about the height. πrh/2 is half of the lateral area, so it’s not correct for this surface.

Think of the side of a cylinder as a curved surface. If you unwrap that curved surface, it becomes a rectangle. The height of that rectangle is the cylinder’s height, h, and the width is the circumference of the base, which is 2πr. The area of that rectangle is width times height, so the lateral surface area is (2πr) × h = 2πrh.

πr^2 is the area of a circle (the base), not the side. πd^2 would be π(2r)^2 = 4πr^2, which isn’t about the height. πrh/2 is half of the lateral area, so it’s not correct for this surface.