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  • The radius r of a right circular cylinder is increasing at the rate of 5 cm/min and its height h, is decreasing at the rate of 4 cm/min. When r = 8 cm and h = 6 cm, find the rate of change of the volume of the cylinder.  

The radius r of a right circular cylinder is increasing at the rate of 5 cm/min and its height h, is decreasing at the rate of 4 cm/min. When r = 8 cm and h = 6 cm, find the rate of change of the volume of the cylinder.

 

 

 

 
 
 
 
 

Answers (1)

Let the increasing rate of radius be \frac{dr}{dt} = 5 cm/ min

& and increasing rate of height be \frac{dh}{dt} = -4 cm/ min

Volume = V = \pi r^2 h

DIfferentiating w.r.t 't': \frac{dr}{dt} = \pi\left(r^2\frac{dh}{dt} + 2hr\frac{dr}{dt} \right )

                                        \begin{align*} \left.\frac{dV}{dt}\right )_{\text {at } r = 8, h = 6} & = \pi\left(64\times -4 + 2\times 6\times 8 \times 5\right ) \\ & = 224\pi \ cm^3/min\end{align*}

\therefore VOlume is increasing at the rate of  224\pi \ cm^3/min.

Posted by

Ravindra Pindel

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