Question

Find the surface area of a cylinder with a height of 5 in and a base radius of 4 in.Use the value 3.14 for it, and do not do any rounding.Be sure to include the correct unit.

Answer 1

The surface area of a cylinder is given by the sum of the lateral area and the area of both basis(the bottom base and the top). The base of a cylinder is a circle, therefore, the area of its base is

`A_b=\pi r^2`

where r represents the radius.

The lateral area of a cylinder is given by the formula

`A_l=2\pi rh`

where r represents the radius and h the height.

The total surface area is:

`S=2A_b+A_l=2\pi r^2+2\pi rh=2\pi r(r+h)`

Using the given values on the text, we have

`S=2\cdot\pi\cdot4(4+5)=8\cdot\pi\cdot9=72\pi=226.08`

The surface area of this cylinder is 226.08 in².