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A rectangular prism with integer side lengths has a height of 3. If the surface area of the prism is equal to \(56\), then what is the volume of the prism?

 Jan 16, 2022
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if the prism's dimensions are 3, x and y, then 2xy + 2(3x) + 2(3y) = 52, taking into account the six rectangular face area totals.

 

It's a matter of experimentation to see which (x,y) ordered pairs satisfy that area relationship. I found that if x=2, y=4, then that works, for area, and therefore the volume is 2(4)(3) = 24 cu units.

 Jan 17, 2022

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