How many 3 inch cubed brownies can fit in a tin that is 9 inches deep by 12 inches wide by 8 inches high?

Answer 1

If I understand the "3 inch cubed," then it's 24.j3h The key here isn't to just do the arithmatic, but instead to think about it logically. Arithmatically, you can fit 32 brownies in there, but that ends up only being in the real world if you smash the mass of those brownies into a new form. The arithmatic of calculated the volume of each (the box and an individual brownie) and seeing how many times the brownie volume goes into the box volume does not take shape into account. Using this problem, the box is 864 square inches and a brownie is 27. If those browneis could be any shape you wanted and the only requirement was that their volume remain 27, then you could fit 32 of them in. But because their shape must always be 3X3X3, or a cube, then you can only fit in 24. The surface of the box is the deepth times width (9x12) and the surface of a brownie is 3X3 (9), so you can fit (12x9)/9=12 brownies per surface. But because the brownies are 3 inches high, and the box is eight, there are only two surfaces. There will be 2 inches of remaining unused height. Thus the answer is 12 + 12 =24