Question

Water flows at the rate of $10m/minute$ through a cylindrical pipe $5mm$ in diameter. How long would it take to fill a conical vessel whose diameter at the base is $40cm$ and depth $24cm$?

Answer 1

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

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

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

Also, given diameter of the conical vessel $=40cm$

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

And depth of the conical vessel $=24cm$

Volume of the conical flask $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times (20{)}^2\times 24=\frac{211200}{21}=10057.14c{m}^3$
Required time to fill the conical flask $=\frac{\text{Volume of the conical vessel}}{\text{Area of the face of pipe}\times \text{Speed of water}}$

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

$=51.20min=51min+\frac{20}{100}\times 60s=51min12s$