Question

A can of tuna has a volume 18pi cm3 and a height of 2 cm. Find the area of the label that wraps around the entire can and does not overlap. Write your answers in terms of pi

Answer 1

The area of the label is
`12\pi\ cm^(2)`

Explanation:

step 1

Find the radius

we know that

The volume of the cylinder (can of tuna) is equal to

`V=\pi r^(2) h`

In this problem we have

`V=18\pi\ cm^(3)`

`h=2\ cm`

substitute and solve for r

`18\pi=\pi r^(2) (2)`

Simplify

`18=r^(2)(2)`

`r^(2)=9`

`r=3\ cm`

step 2

Find the lateral area of the can

The lateral area of the cylinder (can of tuna) is equal to

`LA=2\pi rh`

we have

`r=3\ cm`

`h=2\ cm`

`LA=2\pi (3)(2)=12\pi\ cm^(2)`