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 four corners. write an equation that relates the volume of variables x and y.

Answer 1

Let's denote the side length of the square that is cut out from each corner as xx. When the squares are cut out from each corner and the remaining flaps are folded up to form the open-top box, the dimensions of the base of the box will be 3−2x3−2x by 3−2x3−2x, since xx is cut out from each corner. The height of the box will be yy, which is the length of the flaps that were folded up.

The volume VV of the box can be calculated as the product of its length, width, and height:

V=(3−2x)×(3−2x)×yV=(3−2x)×(3−2x)×y

Simplifying this equation gives the relation between the volume VV and the variables xx and yy:

V=y(3−2x)2V=y(3−2x)2

So, the equation that relates the volume VV to the variables xx and yy is: V=y(3−2x)2V=y(3−2x)2.