Calculus

Find the instantaneous rate of change of the volume V=(1/3) pi r^2 H (all put together) of a cone with respect to the radius r at r=a if the height H does not change.

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  1. Differentiate with respect to r ONLY

    dV/dr = (2/3)pi r H @ r = a
    = (2/3) pi a H

    Usually when you talk about rates it is with respect to time. If you knew the rate that r was increasing, you could multiply it by dV/dr above to get that rate.

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