Question

The radius of a right circular cylinder increases at the rate of $0.1cm/min$, and the height decreases at the rate of $0.2cm/min$. The rate of change of the volume of the cylinder, in $c{m}^3/min.$, when the radius is $2cm$ and the height is $3cm$ is

• A. $-2p$
• B. $-\frac{8\pi }{5}$
• C. $-\frac{3\pi }{5}$
• D. $\frac{2\pi }{5}$

Answer 1

The correct option is D $\frac{2\pi }{5}$

Volume of cylinder $V=\pi r^{2}h$
$\frac{dV}{dt}=\pi (r^2\frac{dh}{dt}+2rh\frac{dr}{dt})$
$\Rightarrow \frac{dV}{dt}=0.4\pi$
$\frac{dV}{dt}=\frac{2\pi }{5}c{m}^3/min$