Question

A cardboard box with a square base and an open top is to be constructed from 108 m2 of cardboard. Express the volume of the box as a function of the length x of the side of the square base.

Answer 1

To express the volume of the box as a function of the length x of the side of the square base, set up an equation using the given area of cardboard. Solve for the height and substitute it into the volume equation.

Step-by-step explanation:

To express the volume of the box as a function of the length x of the side of the square base, we need to find the height of the box. The cardboard box has an open top, so the total area of the cardboard used will be the sum of the area of the square base and the area of the four sides. We can set up an equation:

108 = x^2 + 4xh

where h represents the height. To find the volume, we multiply the area of the base (x^2) by the height (h):

Volume = x^2 * h

We can solve the first equation for h and substitute it into the volume equation to express the volume as a function of x.