Raymond wants to make a box that has a volume of 360 cubic inches. He wants the height to be 10 inches and the other two dimensions to be whole numbers of inches. How many different-sized boxes can he make?

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Answer 1 · 2016-04-01T03:03:22

The formula for volume is #v = L xx W xx H#

#360 = L xx W xx 10#

#360/10 = L xx W#

#36 = L xx W#

Now, we must find all the factors of 36. Since whether L is 36 and W is 1 or L is 1 and w = 36, we'll consider the pair [36, 1] as one.

#36 = [36, 1], [9, 4], [12, 3], [18, 2], [6, 6]#

Counting the pairs, we get 5 possible dimensions, all giving a volume of 360 cubic inches.

Hopefully this helps!