Write an expression for the volume in terms of x and y?

“A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Let x denote the length of the side of the square being cut out. Let y denote the length of the base.

Write an expression for the volume V in terms of x and y”

First, what do they mean by ” Let y denote the length of the base”? The base of what? The box of the square cardboard being used to make the box? And since the cardboard is a square, the width must be equal to lenght, so x=3, right?

The answer I got was V = (y^2)((x-y)/-2)

Apprently its wrong….

Thanks!

Answer:

The Best Answer for Write an expression for the volume in terms of x and y?

Yes, you are wrong, but it’s an easy mistake to make, especially if you don’t know what “y” stands for. Look at the diagram below. It is the flat cutout of the 3′ square piece of cardboard. When you cut out the squares at each corner, and fold the box along the 4 green lines, the resulting dimensions of the base of the box will be dimension “y”, and the height of the box will be dimension “x”.

The volume of the box is then V = x(y^2)

Now you also know that y = 3 – 2x, and if you’re in calculus, you can determine the value of x that will result in the max. volume of the box.