Question

Faith wants to wrap the bottom and outside of a can with wrapping paper to make a holder for pens and pencils. She needs to know the surface area of the outside of the can in the picture below................?

Answer 1

Please see below.

Explanation:

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Part `A`

`pir^2` is the formula for the area of a circle which means you can use it to calculate the area of the top or the bottom of the can.

`2pirh` is the formula for the area of the side of the can. Because that area is equal to the perimeter of the top (or bottom) of the can multiplied by the height of the can.

The perimeter of the top or bottom is the perimeter of a circle whose formula is `2pir` and `h` is the height of the can.

We can plug in the measurements from the picture:

`Area_(outside)=pi(4)^2+2pi(4)(9)=16pi+72pi=88pi=276.5` `cm^2`

Part `B`

The reason is that the top of the can has to be open to be used as a pencil holder. Therefore, you do not have to include the area of the top which is `pir^2`.