Water flows at the rate of 10 m min-1 through

Given, speed of water flow = 10 m min-1 = 1000 cm/min

and diameter of the pipe $=5 \mathrm{~mm}=\frac{\mathrm{s}}{10} \mathrm{~cm}$

$\therefore \quad$ Radius of the pipe $=\frac{5}{10 \times 2}=0.25 \mathrm{~cm}$

$\therefore$ Area of the face of pipe $=\pi r^{2}=\frac{22}{7} \times(0.25)^{2}=0.1964 \mathrm{~cm}^{2}$

Also, given diameter of the conical vessel $=40 \mathrm{~cm}$

$\therefore$ Radius of the conical vessel $=\frac{40}{2}=20 \mathrm{~cm}$

and depth of the conical vessei $=24 \mathrm{~cm}$

$\therefore \quad$ Volume of conical vessel $=\frac{1}{3} \pi r^{2} h=\frac{1}{3} \times \frac{22}{7} \times(20)^{2} \times 24$

$=\frac{211200}{21}=10057.14 \mathrm{~cm}^{3}$

$\therefore$ Required time $=\frac{\text { Volume of the conical vessel }}{\text { Area of the face of pipe } \times \text { Speed of water }}$

$=\frac{10057.14}{0.1964 \times 10 \times 100}$

$=51.20 \mathrm{~min}=51 \mathrm{~min} \frac{20}{100} \times 60 \mathrm{~s}=51 \mathrm{~min} 12 \mathrm{~s}$