Explain circumference, area, and volume formulas using informal arguments such as dissection, Cavalieri, and limits.
Recover pyramid volume from a matched prism
Problem
A triangular prism with base area \(36~\text{cm}^{2}\) and height \(10~\text{cm}\) is decomposed into \(\text{three}~\text{equal}\text{-}\text{volume}~\text{pyramids}\). Calculate the prism volume, divide by the equal-piece count, and state \(\text{one}~\text{pyramid}\)'s volume and the resulting \(V~=~(1/3)Bh\) relationship.
The matched prism provides an easier whole whose volume comes from base area and perpendicular height. We’ll find that whole first, use the stated decomposition to determine one equal share, and then generalize the equal-piece relationship so the pyramid factor applies to any matched base area and height.
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