Question

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?

Answer 1

The length of each side will be:

`x=sqrt(163)-1~~11.77 " inches"`

Explanation:

The area of a box is:

`A_"box" = "area top" + "area bottom" + (4*"area 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 `x^2` and the bottom is `x^2` and the 4 edges are `1*x`, finally the area `A=324`

`A_"box" = "area top" + "area bottom" + (4*"area sides")`

`324 = x^2 + x^2 + 4x`

`2x^2 + 4x = 324`

`2(x^2 +2x) = 324`

`x^2 + 2x =162`

`x^2 + 2x +1=162 +1`

complete the square:

`(x+1)^2 = 163`

`sqrt((x+1)^2) = +-sqrt(163)`

x+1 = +-sqrt(163)#

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

`x=sqrt(163)-1~~11.77 " inches"`