Answer:
[tex]0.0727 cm\: per\: second[/tex]
Step-by-step explanation:
The Volume of the cylinder is constant
Volume of a cylinder, [tex]V=\pi r^2h[/tex]
Given:
[tex]\frac{dh}{dt}=0.8 cm/sec\\ r=2cm\\h=11cm\\\frac{dr}{dt}=?[/tex]
[tex]\frac{dV}{dt}=\pi r^2 \frac{dh}{dt} + 2\pi r h\frac{dr}{dt}[/tex]
[tex]0=\pi* 2^2*0.8 + 2\pi*2*11\frac{dr}{dt}\\0=3.2\pi+44\pi\frac{dr}{dt}\\44\pi\frac{dr}{dt}=-3.2\pi\\\frac{dr}{dt}=\frac{-3.2\pi}{44\pi} \\\frac{dr}{dt}=-0.0727 cm\: per\: second[/tex]
The radius is decreasing at a rate of [tex]0.0727 cm\: per\: second[/tex]
