Question

A box with a square base and no top is to be made from a square piece of carboard by cutting 8 in. squares

from each corner and folding up the sides. The box is to hold 28800 in'. How big a piece of cardboard is
needed?

Answer 1

To determine the size of the square cardboard needed to create a box with a volume of 28800 cubic inches, after cutting out 8 inch squares from each corner, set up and solve the equation (x - 16)(x - 16)8 = 28800.

Step-by-step explanation:

The subject of this question is Mathematics, specifically involving geometry and algebra to solve a real-world application problem about constructing a box from a square piece of cardboard. To find the necessary size of the cardboard to create a box that holds 28800 cubic inches, we must first consider the size of the squares to be cut from each corner, which are 8 inches on each side. We'll let the side of the cardboard be x. The new dimensions after cutting the squares will be x - 2(8) or x - 16 inches for both the length and the width, as the base of the box is square. The height of the box is 8 inches (the side length of the cut out squares). Therefore, the volume of the box is (x - 16)(x - 16)8 cubic inches.

To find x, we set up the equation (x - 16)(x - 16)8 = 28800 and solve for x. Simplifying the equation, we need to solve a quadratic equation to find the dimensions of the cardboard. By performing these steps, we can determine the original size of the square cardboard needed to create the box.