Answer:
252π or 791.7 mm³/h
Step-by-step explanation:
The volume of a cylinder is given by
[tex]V = \pi r^2h[/tex]
We desire to find the volume rate, that is,[tex]\dfrac{dV}{dt}[/tex]
[tex]\dfrac{dV}{dt} = \dfrac{dV}{dr}\cdot\dfrac{dr}{dt}[/tex]
dr/dt is the rate of change of the radius which is 7 mm/h.
dV/dr is derived by differentiating the volume equation, yielding
[tex]\dfrac{dV}{dt} = 2\pi rh[/tex]
At r = 12 mm and h = 1.5 mm,
[tex]\dfrac{dV}{dt} = 2\pi\times12\times1.5\times7 = 252\pi = 791.7[/tex]
