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...

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.