Surface area cylinder

The surface area of any shape can be found by adding together the surface areas of its parts.

Cylinder

Taking apart a cylinder by adding 2 circles and a rectangle

If you always imagine pulling apart the cylinder and drawing it out you can clearly see that the areas are one rectangle and two areas of a circle (the top and bottom).

The rectangle

To find the area of the rectangle its height multiplied by length

The area of the rectangle is Height = `h` multiplied by Length = `2\pir`

Area of rectangle = `h\times\2\pir`

The circle areas are:

First find the radius then its pie r squared as there are 2 circles is 2 pie r squared

Area = `\pir^2`

And because there are two circles

Area = `2\pir^2`

Summary

Area of a cylinder:

`h2\pir + 2\pir^2`

Example 1

Ted has a cylinder of height 15 cm and diameter 8 cm. He calculates the curved surface area as
`2×\pi\times8×15`. Explain what he has done wrong.

Answer:

He used the diameter not the radius (Circumference = `2\pir`)

Or

He incorrectly multiplied by 2 when calculating the circumference (Circumference = `\pid`).