GCSE(F), GCSE(H),

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`

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

Answer: 3996.1 cm^{2}

The area of each of the ends = π*r*^{2} = π x 6^{2} = 36π

There are two ends: 2 x 36π = 72π

The area of the length = 2π*rl* = 2π x 6 x 100 = 1200π

Total area = 1200π + 72π = 3996.1 cm^{2} (to 1 dp)

2. A cylinder has a surface area of 1000 cm^{2} and a diameter of 5cm. What is the length of the cylinder?

Answer: 61.2 cm

Area = 2π*rl* + 2π*r*^{2}

The radius is half of the diameter = 2.5cm

1000 = 2 x π x 2.5 x *l* + 2 x π x 2.5^{2}

1000 = 15.708*l* + 39.270

960.730 = 15.708*l*

*l* = 61.162. or 61.2cm to 1dp

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