# Find the Surface Area of a Cylinder

In this worksheet, students will calculate the surface area of cylinders given their diameter and height.

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Use 3D Shape Knowledge to Solve Problems

Popular topics:   Area worksheets, Geometry worksheets

Difficulty level:

#### Worksheet Overview

Look at this cylinder.

Its net is made up of two circles and a rectangle.

In the two formulae below, r is the radius and d is the diameter.

The area of a circle is πr

The circumference of a circle is πd

Look at these diagrams to see that the base of the rectangle has the same length as the circumference of the circle.

So the surface area is the area of the two circles plus the area of the rectangle.

The area of the two circles = 2πr2

The area of the rectangle =  πdh  or we can write 2πrh (because the diameter is the radius x 2)

Surface Area = 2πr2 + πdh = 2πr2 + 2πrh

Example

Find the surface area of this cylinder in cm2 to 3 significant figures.

Answer

Diameter = 6 cm

Radius = 6 ÷ 2 = 3 cm

Height = 12 cm

Surface Area = 2πr2 + 2πrh  = 2 x π x 32 + 2 x π x 3 x 12 = 282.74 ≈ 283 cm2 (3 s.f.)

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