Question

Water flows at the rate of $15m$ per minute through a cylindrical pipe, having the diameter $20mm$. How much time (in min) will it take to fill a conical vessel of base diameter $40cm$ and depth $45cm$?

Answer 1

Radius of the pipe $=\frac{20}{2}mm=10\times \frac{1}{10}cm=1cm$

Speed of water $=15m/min=1500cm/min$

Volume of water that flows in $1$ minute

$=\pi \times r^{2}h=\frac{22}{7}\times 1\times 1\times 1500$${cm}^3/min=\frac{33000}{7}{cm}^3/min$

Radius of conical vessel $=\frac{40}{2}=20cm$;

Depth $=45cm$

Therefore,

Capacity of the vessel $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times (20{)}^2\times 45=\frac{132000}{7}{cm}^3$

Therefore, Time required to fill the vessel $=\frac{\text{Capacity of the vessel}}{\text{Volume of water flowing per minute}}$

$\frac{132000/7}{33000/7}$ min $=4$ min