Question

A box with an open top is to be constructed from a rectangular prece of cardboard witn aimensions n by cutting out equal squares of side x at each corner and then folding up the sides: Express the volume V of the box as a function of x.

Answer 1

To express the volume V of the box as a function of x, the dimensions of the resulting box can be determined by subtracting 2x from the original dimensions. The volume can then be calculated by multiplying the dimensions.

Step-by-step explanation:

To express the volume V of the box as a function of x, we need to determine the dimensions of the box.

When squares of side x are cut out of each corner of the rectangular piece of cardboard, the dimensions of the resulting box will be (n-2x) by (n-2x) by x, where n represents the original dimensions of the rectangular piece of cardboard. This is because x is cut out from each corner, reducing the length and width of the rectangular piece by 2x.

The volume of the box can be calculated by multiplying the length, width, and height, which gives us V = (n-2x)(n-2x)x = x(n-2x)(n-2x).