Surface Area of a Cylinder

## Surface Area of a Cylinder

A cylinder is a circular prism. The surface area of a cylinder consists of the two ends, plus the area given by its length between these two ends.

The net of the cylinder, shown above, is the shape that is obtained when the cylinder is unwound and laid flat. It consists of two circular ends and a rectangular shape. The rectangular shape is the length of the cylinder, and the width that is equal to the perimeter of the circular ends.

The surface area of a cylinder of radius r and length l is 2πrl + 2πr^2

## Example 1

A cylinder has a radius of 6cm and a length of 1m. What is the surface area of the cylinder?

 area of one end = πr^2 = pi(6)^2 = 36pi Two ends 36pi xx 2 = 72pi Area of length = 2πrl = 2π(6)(100) = 1200pi Total Area = 1200π + 72π = 3996.1

 Area = 2πrl + 2πr^2 1000 = 2 xx π xx 2.5 xx l + 2 xx π xx 2.5^2 1000 = 15.708l + 39.270 960.730 = 15.708l 61.162 = l