A Ruled Prism

Calculus Level 5

Define a ruled prism to be a solid with 2 parallel faces and a ruled surface joining the 2 parallel faces continuously and without overlap.

Given that you know the perpendicular distance between the 2 parallel faces and the areas of \(n\) cross-sections of the ruled prism, what is the minimum \(n\) such that you can know the exact volume of the ruled prism?

(You can choose which cross-sections to find the area of.)

The diagram above is an example of a ruled prism with a square and a circle as the parallel faces and a ruled surface connecting them.


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