Asked by bgfc
What is the formula for the volume of a cylinder with radius r and height h? In 3–5 sentences, describe an informal argument for this volume formula.(4 points) simple
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GPT-5 mini
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V = π r^2 h.
Informal argument: A cylinder can be thought of as a stack of many very thin circular discs, each disc having area π r^2. If each disc has a tiny thickness Δh, its volume is approximately π r^2 Δh, and adding up all the discs from bottom to top gives π r^2 h. Equivalently, like a prism whose cross‑sectional area is the base area, the volume equals base area times height.
Informal argument: A cylinder can be thought of as a stack of many very thin circular discs, each disc having area π r^2. If each disc has a tiny thickness Δh, its volume is approximately π r^2 Δh, and adding up all the discs from bottom to top gives π r^2 h. Equivalently, like a prism whose cross‑sectional area is the base area, the volume equals base area times height.
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