Water in an inverted cone satisfies $$r=\frac h2.$$ The area $A$ of the horizontal water surface i

Question

Water in an inverted cone satisfies $$r=\frac h2.$$ The area $A$ of the horizontal water surface increases at $3\pi\text{ cm}^2/\text{s}$. When $h=6\text{ cm}$, find: $\dfrac{\mathrm{d}h}{\mathrm{d}t}$; $\dfrac{\mathrm{d}V}{\mathrm{d}t}$.

Accepted Answer

(a) $\frac{\mathrm{d}h}{\mathrm{d}t}=1\text{ cm/s}$; (b) $ \frac{\mathrm{d}V}{\mathrm{d}t}=9\pi\text{ cm}^3/\text{s}$.

Differentiation

Differentiation

Solution:

Solution locked