A pizza packages its circular pizzas in a cardboard box. The boxes are formed by folding in 1" squares from the corners of the cardboard. If the volume of the box is 324 cubic inches, what are the dimensions of the box, in inches? Draw it?

A pizza packages its circular pizzas in a cardboard box. The boxes are formed by folding in 1" squares from the corners of the cardboard. If the volume of the box is 324 cubic inches, what are the dimensions of the box, in inches?

1 Answer
May 27, 2018

The length of each side will be:

x=163111.77 inches

Explanation:

The area of a box is:

Abox=area top+area bottom+(4area sides)

We will assume that the box is square so l=w and has a top and bottom.

we'll call the unknown length x

so the to is x2 and the bottom is x2 and the 4 edges are 1x, finally the area A=324

Abox=area top+area bottom+(4area sides)

324=x2+x2+4x

2x2+4x=324

2(x2+2x)=324

x2+2x=162

x2+2x+1=162+1

complete the square:

(x+1)2=163

(x+1)2=±163

x+1 = +-sqrt(163)#

we can ignore the negative root because a length can't be negative:

x=163111.77 inches