Algebra Word Problem

Question

Draw a rectangle that is 20 by 18. From this rectangle we can make a box without a lid by cutting a square from each corner and then folding up the flaps. If you cut off a 1 inch by 1 inch square, what is the volume of the box? If you cut off a 2 inch by 2 inch square, what is the volume. What is the maximum possible volume?

Answer 1

This problem can be started by drawing a "box without a lid" with the given dimensions. After you draw and mark the box, visualize how much is being subtracted from each side when you cut out the 1x1 squares from the corners. The volume of any box with or without the lid is just the product of all three values. Length x width x height. In the first case, since the squares being cut out are 1x1, you would subtract 2 from each side. The volume would be now 16x18x1 = 288 cubic inches. In the second case, it is very similar except you are subtracting 4 from each side and going up 2 inches instead of 1. The volume would be 14x16x2 = 448 cubic inches.