Asked by Void<3
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)
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GPT-5 mini
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V = π r^2 h.
Informal argument: the cylinder can be thought of as a stack of very thin circular disks, each with area πr^2. Adding up the volumes of those disks (area × thin thickness) over the height h gives volume = ∫_0^h πr^2 dz = πr^2 h. Equivalently, like any prism the volume equals base area (circle of area πr^2) times height.
Informal argument: the cylinder can be thought of as a stack of very thin circular disks, each with area πr^2. Adding up the volumes of those disks (area × thin thickness) over the height h gives volume = ∫_0^h πr^2 dz = πr^2 h. Equivalently, like any prism the volume equals base area (circle of area πr^2) times height.
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