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A company makes concrete stones in different sizes. Each stone has a volume of 360 cubic inches and a height of 3 inches. The stones have different lengths and widths. No stones have a length or width of 1 or 2 inches. How many different paving stones, each with a different-size base, have a volume of 360 cubic inches?

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sylvain96

Answer:

6 different

Step-by-step explanation:

If the total volume is 360 cubic inches and the height is fixed at 3 inches, that leaves a total area of 120 square inches (x3 inches = 360 cubic inches).

Let's assume the measurements have to integer (whole numbers), otherwise there could be an infinite number of different sizes (like width of 2.1, 2.2, 2.3, and so on).  We also know that the minimum size in any dimension is 3 inches.

So, how many combinations of numbers greater than 2 can we make to have a product of 120?  Let's start at 3 and go up.

3 x 40, 4 x 30, 5 x 24, 6 x 20, 8 x 15, 10 x 12

Past 10 in the first number, we return to the same dimensions, but in reverse order (12x10, 15x8, and so on), so they wouldn't be different.

So, the number of different size base is 6.

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