Explain circumference, area, and volume formulas using informal arguments such as dissection, Cavalieri, and limits.
Build prism and cylinder volume from congruent layers
Problem
A right prism has triangular cross-section area \(18~\text{cm}^{2}\) at every level and perpendicular height \(7~\text{cm}\). Use the congruent-layer interpretation of \(V~=~Bh\) to calculate its volume with cubic units.
A prism’s volume can be organized as a constant cross-sectional area repeated through a perpendicular distance. We’ll identify the area shared by every parallel layer, distinguish the height from any slanted edge, multiply area by that accumulation distance, and use the units to confirm that the quantity is a volume.
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