Water flows at the rate of 10 m per minute through a cylindrical pipe with internal diameter 2 cm. How long (in minutes) would it take to fill completely aconical vessel whose radius is 50 cm, and depth 45 cm?

Let the time be ‘t’ minutes volume of conical vessel is $\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$
${\mathrm{V}}_{\mathrm{conical}\mathrm{vessel}}=\frac{1}{3}\times \mathrm{\pi }\times {\left(50\right)}^2\times 45$
Volume thrown by cylindrical pipe $={\mathrm{\pi r}}^2\mathrm{h}$
$=\mathrm{\pi }\times {\left(1\right)}^2\times \mathrm{h}=\mathrm{\pi h}$
According to question,
$\begin{array}{l}\mathrm{\pi h}=\frac{\mathrm{\pi }}{3}(50{)}^{2}45\\ \mathrm{h}=2500\times 15\\ \mathrm{t}=\frac{\text{ dis tan ce }}{\text{ speed }}=\frac{2500\times 15}{1000}\\ =\frac{75}{2}=37.5\text{ minutes }\end{array}$