Question

How much cardboard is needed to make the single slice pizza box shown

Answer 1

Step-by-step explanation

We must find the amount of cardboard needed to make a slice of pizza box which basically means finding the surface area of the piece of box shown. This is composed of five faces divided in three groups:

- Two equal triangular faces with a base of 6.7 in and a height of 11 in.

- Two equal rectangular faces with a base of 11.5 in and a height of 1 in.

- A single rectangular face with a base of 6.7 in and a height of 1 in.

The area of the piece of box is given by the sum of the areas of the 5 faces so let's find the area of the faces of each group.

The area of a triangle is given by half the product of the length of its base and its height. Then the area of each triangular face is:

`A_t=(6.7*11)/(2)=36.85`

So each triangular face has an area of 36.85 in².

The area of a rectangle is given by the product of its base and height. Then for the pair of equal rectangular faces we have:

`A_(r1)=11.5*1=11.5`

So each of these two faces has an area of 11.5 in².

The area of the remaining rectangular face is then given by:

`A_(r2)=6.7*1=6.7`

So the area of the last face is 6.7 in².

Then the total surface area is given by the sum of the areas of the 5 faces. Then we get:

`A=2A_t+2A_(r1)+A_(r2)=2*36.85+2*11.5+6.7=103.4`Answer

Then the answer is 103.4