Rates of change · manipulative

Related rates: draining cone

Water leaves an inverted cone at a known volume rate. Similar triangles link radius to height — the chain rule multiplies those rates to give dh/dt.

Scrub h while paused · Play integrates dh/dt from the volume rate

Animate

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Similar triangles
nested tank / water triangles + ratio
Elapsed time
t while draining

Tank & rates

10
5
6
−2

Link and differentiate