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

Answer:

The area of the label is $12\pi\ cm^{2}$

Step-by-step 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

$r=3\ cm$

$h=2\ cm$

$LA=2\pi (3)(2)=12\pi\ cm^{2}$