Answer:
276 square cm
Step-by-step explanation:
We are solving for the lateral area of the cylinder soup can. This is the area of its side (NOT its bases).
The side of a can is a rectangle, so its area is:
[tex]A=l\cdot w[/tex]
where [tex]l[/tex] = length, [tex]w[/tex] = width.
We are given that: [tex]l = 11\text{ cm}[/tex].
We need to solve for the rectangle's width, which is the same as the circumference of the circle base:
[tex]C = \pi d =w[/tex]
↓ plugging in the given [tex]d=8\text{ cm}[/tex]
[tex]w = 8\pi[/tex]
Plugging these dimensions in the above area formula:
[tex]A=11 \cdot 8\pi[/tex]
[tex]\boxed{A\approx276\text{ cm}^2}[/tex]
So, the label that covers the lateral area of the soup can has an area of approximately 276 square centimeters.
