Answer:
The area of the label is [tex]12\pi\ cm^{2}[/tex]
Step-by-step explanation:
step 1
Find the radius
we know that
The volume of the cylinder (can of tuna) is equal to
[tex]V=\pi r^{2} h[/tex]
In this problem we have
[tex]V=18\pi\ cm^{3}[/tex]
[tex]h=2\ cm[/tex]
substitute and solve for r
[tex]18\pi=\pi r^{2} (2)[/tex]
Simplify
[tex]18=r^{2}(2)[/tex]
[tex]r^{2}=9[/tex]
[tex]r=3\ cm[/tex]
step 2
Find the lateral area of the can
The lateral area of the cylinder (can of tuna) is equal to
[tex]LA=2\pi rh[/tex]
we have
[tex]r=3\ cm[/tex]
[tex]h=2\ cm[/tex]
[tex]LA=2\pi (3)(2)=12\pi\ cm^{2}[/tex]
