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11111nata11111 [884]
3 years ago
9

The part of a cylindrical soup can that is covered by the label is 8.5 cm tall and has a diameter of 6.5 cm. What is the area of

a label that covers the entire side of the can and that need a 0.8-cm overlap to glue the ends of the label? Round to the nearest tenth.
Mathematics
1 answer:
julia-pushkina [17]3 years ago
5 0

Answer:

180.4~cm^2

Step-by-step explanation:

<u>Surface Area</u>

The surface area of a cylinder of height h and radius r is given by:

A=2\pi rh

It only covers the lateral side of the cylinder. If both the top and the bottom sides are to be included, then:

A=2\pi rh+2\pi r^2

The label will cover only the lateral side of the soup can that has a height of h=8.5 cm and a diameter of 6.5 cm. We need to calculate the radius which is half of the diameter r=6.5 cm / 2 = 3.25 cm.

Now we calculate the side area of the can:

A=2\pi (3.25)(8.5)

A=173.6~cm^2

We need to add the 0.8 cm overlap to the total area already calculated. This overlap has 0.8 cm of width and 8.5 cm of height, so this overlap area is:

A_o= 0.8*8.5=6.8~cm^2

The total area of the label is:

A=173.6~cm^2+6.8~cm^2=180.4~cm^2

The area of the label is \mathbf{180.4~cm^2}

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