Question

Find the rate of change of the volume of a cone with respect to the radius of its base​

Answer 1

V=13πr2h Differentiate implicitly with respect to t. ddt(V)=ddt(13πr2h)= 13πddt(r2h). We'll need the product rule on the right .

Answer 2

Find

Find the rate of change of the volume of a cone with respect to the radius of its base

ANSWER

we know that the volume of the cone

$v = \frac{1}{3} {\pi}^{2}h$

The main objective to find the rate of change of the volume w.r.t the radius of the cone.

So, differentiate with respect to r

$\frac{dv}{dr} = \frac{d}{dr} (\frac{1}{3} {\pi}^{2}h)$

$\frac{1}{3} \pi \: h( \frac{d}{r} \times {r}^{2} )$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{1}{3} \pi \: h \times 2r$

$\: \: \: \: \: \: \: \: \: \: \: \: \frac{1}{3} \pi \: h \times 2r$

$\: \: \: \: \: \: \: \: \: \: \: \: \frac{2}{3} \pi \: rh$

Hence, this is the rate of change of the volume of cone with respect to r.

Hope this will help you..

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