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?

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2 Answers
May 13, 2018

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.

Original DrawingOriginal Drawing

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.

May 13, 2018

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