You want to make a conical paper hat with a slant height of 14" and a base circumference of 16". The bottom of the cone is open. How many square inches of paper will the hat use?

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We are given the slant height(l) and circumference of the cone(c).

We need to find the curved surface area of the cone , since the bottom of the cone is open.

Circumference of the cone (c)=`2pir`

where r is the radius of the base of the cone.

So, `2pir=16`

`=>r=16/(2pi)`

`rArrr=8/pi` ...

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We are given the slant height(l) and circumference of the cone(c).

We need to find the curved surface area of the cone , since the bottom of the cone is open.

Circumference of the cone (c)=`2pir`

where r is the radius of the base of the cone.

So, `2pir=16`

`=>r=16/(2pi)`

`rArrr=8/pi`    ----------(1)

Now the curved surface area of the cone (A) can be calculated as,

`A=pirl`  

Plug the values of r from (1) and l in the above formula to get the area,

`A=pi*8/pi*14`  

`A=8*14`

`A=112`

Hence 112 square inches of paper will be required for making the hat.

Approved by eNotes Editorial Team