Suppose there are n rectangular prisms stacked on top of each other in various ways to form one solid. Each has l = w and a height of h. Using Cavalieri's principle, what is the volume of the solid?

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Mathematics

Dee

27 October, 09:21

Suppose there are n rectangular prisms stacked on top of each other in various ways to form one solid. Each has l = w and a height of h. Using Cavalieri's principle, what is the volume of the solid?

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Cocoa · Answer 1

The volume of the resulting solid will be the volume of one rectangular prism times n.

The the volume of a rectangular prism is V=lwh. But since l=w (cross-section is a square), we now have V=l²h.

The volume of the resulting solid will be V = nl²h or V = nw²h.