Answer:
dr/dt = -3/44 cm/s
Step-by-step explanation:
The volume of a cylinder is given by ...
V = πr²h
Differentiating with respect to t (for constant volume), we get ...
0 = π(2rh·dr/dt + r²·dh/dt)
Solving for dr/dt, we have ...
dr/dt = dh/dt(-r²/(2rh)) = (dh/dt)(-r/(2h))
Filling in the given numbers gives ...
dr/dt = (0.5 cm/s)(-3 cm)/(2·11 cm)
dr/dt = -3/44 cm/s
