Final answer:
To find the volume of a box with a square base and open top, multiply the area of the base by the height. Set up the equation x^2 * h = 62500 and solve for x. Calculate the height of the box using the formula h = 62500 / x^2.
Step-by-step explanation:
To find the volume of a box with a square base and open top, we need to multiply the area of the base by the height. Since the base is square, the area is equal to the length of one side squared. Let's call the length of one side x. The volume of the box is x^2 * h. We are given that the volume is 62500 cubic centimeters, so we can set up the equation x^2 * h = 62500. This is a quadratic equation, and we need to solve for x.
Let's rewrite the equation in terms of h: h = 62500 / x^2. Now, we can substitute this expression for h into the formula for the volume of a cylinder to find the relationship between x and the height of the box.
Once we have the value of x, we can calculate the height of the box using the formula h = 62500 / x^2.