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Home » The volume \( V \) of a cone is given by the formula: - Ready Digital AB

The volume \( V \) of a cone is given by the formula: - Ready Digital AB

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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📌 Assume volume at any time: V = w(t) × h(t) × l (fixed length). But length unknown.

📌 Alternate: assume the rate of volume increase arises from expansion. But simpler: assume length is constant and expands with width and height? Not realistic.

📌 Better: suppose the sensor grid expands in width and height independently, but length is fixed. Still ambiguous.

📌 Assume: the volume is growing due to dwid/dt and dhi/dt, and length is constant. Let le latent.

📌 VDot = (dw/dt)(h)(l) + w(dh/dt)(l) + w×h(dl/dt)? But dl/dt not defined.

📌 Assume length is constant, so only dw/dt and dh/dt contribute to dV/dt.

📌 Then dV/dt = (dw/dt)(h)(l) + w(dh/dt)(l) = l [ (dw/dt)h + w(dh/dt) ]

📌 But l unknown.

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