How do you find $\frac{d V}{d t}$ $(dV)/dt$ if $V = \frac{1}{3} π r^{2} h$ $V=1/3pir^2h$ ?

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Answer 1 · 2016-10-21T03:07:58

$\frac{d V}{d t} = \frac{1}{3} π (2 r \frac{d r}{d t} h + \frac{d h}{d t} r^{2})$ $(dV)/dt=1/3pi(2r(dr)/dth+(dh)/dtr^2)$

Use Implicit Differentiation where each where each factor is differentiated with respect to time, t.

$\frac{d V}{d t} = \frac{1}{3} π (2 r \frac{d r}{d t} h + \frac{d h}{d t} r^{2})$ $(dV)/dt=1/3pi(2r(dr)/dth+(dh)/dtr^2)$

How do you find (dV)/dtdVdt(dV)/dt if V=1/3pir^2hV=13πr2hV=1/3pir^2h?