Question

A box without a top is to be made from a rectangular piece of cardboard, with dimensions 8 in. by 10 in., by cutting out square corners with side length x and folding up the sides. Write an equation for the volume V of the box in terms of x?

Answer 1

The volume of this box will be `4x(5-x)(4-x)` while `x<=4`.

Explanation:

We are constructing a right rectangular prism, with the dimensions `10-2x` by `8-2x` by `x`.

The volume of this box will be the product of its dimensions or `(10-2x)(8-2x)x=4x(5-x)(4-x)` but `x<=4`.

Answer 2

Length of the box `L=8-2x` in

Width of the box `W=10-2x` in

Height of the box `H=x` in

Volume of the box

`V=LxxWxxH=(10-2x)(8-2x)x" ""in"^3`

where `x<4` in