You want to make a rectangular box, open at the top, by cutting the same size square corners out of a rectangular sheet of cardboard and then folding up the sides. the cardboard measures 11 in. by 14 in. what are the dimensions of the box that will have greatest volume if the possible corner cuts measure 1 in., 2 in., 3 in., or 4 in.?

2 in.

Step-by-step explanation:

If we cut squares from all 4 corners and make it into a open rectangular box, the length of the square cut will become the height of the rectangular prism.

If we cut 1 inch side square:

The 11 inch side will become 11 - 2(1) = 9 and 14 inch side will become 14 - 2(1) = 12. Height is 1. So Volume would be 9 * 12 * 1 = 108

If we cut 2 inch side square:

The 11 inch side will become 11 - 2(2) = 7 and 14 inch side will become 14 - 2(2) = 10. Height is 2. So Volume would be 7 * 10 * 2 = 140

If we cut 3 inch side square:

The 11 inch side will become 11 - 2(3) = 5 and 14 inch side will become 14 - 2(3) = 8. Height is 3. So Volume would be 5 * 8 * 3 = 120

If we cut 4 inch side square:

The 11 inch side will become 11 - 2(4) = 3 and 14 inch side will become 14 - 2(4) = 6. Height is 4. So Volume would be 3 * 6 * 4 = 72

Hence, the greatest volume is when we cut 2 inch side square.

i think the amount would be $140.62