This question is asking us to calculate the lateral area of a cone. The lateral area of a cone (L) can be found using the following formula:

`L=pi*r*l`

where r is the radius of the cone and l is the slant height of the cone. We are told to use 3.14 to approximate pi (`pi`).

We are told our cone has a diameter (D) of 3 inches and a slant height of 6 inches. Diameter is defined as twice the radius.

`D=2*r`

So we can calculate the radius of our cone as follows:

`r=D/2=3/2=1.5` in

Now that we know the radius is 1.5 inches, we can calculate the lateral area:

`L=pi*r*l=pi*1.5*6=pi*3=3.14*3=9.42` in^2

The lateral area of the cone is 9.42 square inches. So, in order to make a paper snow cone cup, you will need approximately 9.42 square inches of paper.

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