An open box is to be constructed from a rectangular piece of cardboard which measures 18 inches by 20 inches. To make the box a square shaped cut is made at each corner of the rectangle and the sides folded up. Each square cut must be a whole number of inches on each side. Determine what size cut will result in the box with the greatest volume.
2007-10-29 14:49:11 · 1 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Well, the greatest volume is usually found in a cubic box, but in this case, we might be cutting away a lot of cardboard. If we cut 1 square inch out of each corner, and fold thge sides up, we have a box 16x18x1, or 288 cubic inches. How about 2 inch square from each corner? 14x16x2 = 448 cubic inches, aha! OK, shoot for 6 inch square corners, 6x8x6 =288. Oops. 3 inch square,
12x14x3 =504, 4 inch square, 10x12x4=480, 5 inch square, 8x10x5=400
3 inch square cutout seems to work best.
2007-10-29 15:10:53 · answer #1 · answered by Computer Guy 7 · 0⤊ 0⤋