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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.

Net of a cylinder (for Surface Area)

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`

Answer: 3996.1 cm2

Example 2

A cylinder has a surface area of 1000 cm2 and a diameter of 5cm. What is the length of the cylinder?

The radius is half of the diameter = 2.5cm

Answer: 61.2 cm

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`