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How many different rectangular prisms can you make with a volume of 24 cubic units?
Wiki User
∙ 11y ago
Infinitely many.
For example, let a be any positive number less than cuberoot(24) = 2.88 approx.
Let b be any number such that a < b and b < sqrt(24/a).
And let c = 24/(a*b)
Then a rectangular prism with sides of lengths a, b and c will all be different and each will have a volume of 24 cubic units. And since the choice of two of the sides is arbitrary, the number of such prisms is infinite.
The conditions placed on the measures are simply to ensure that the three measures are in non-decreasing order. This ensures that a prism of sides 2*4*3 will not appear in the list, having already been recorded as a 2*3*4 prism.
Wiki User
∙ 11y ago
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