Water flows from a cylinder of radius $3\text{ cm}$ into an inverted cone whose water radius and d

Question

Water flows from a cylinder of radius $3\text{ cm}$ into an inverted cone whose water radius and depth satisfy $r=h/2$. The water depth in the cylinder falls at $\dfrac29\text{ cm/s}$. Find: the inflow rate into the cone; the rate of increase of the cone’s water depth when $h=4\text{ cm}$.

Accepted Answer

(a) Inflow $=2\pi\text{ cm}^3/\text{s}$ ;(b) $ \frac{\mathrm{d}h}{\mathrm{d}t}=\frac12\text{ cm/s}$.

Differentiation

Differentiation

Solution:

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