Question

A farmer connects a pipe of internal diameter $20cm$ from a canal into a cylindrical tank in his field that is $10m$ in diameter and $2m$ deep. If water flows through the pipe at the rate of $3km/hr$, in how much time will the tank be filled?

Answer 1

Solution:
Given,
Internal diameter of pipe$=20cm$
Diameter of cylindrical tank$=10m$
Height of the tank $=2m$
Rate of water flow$=3km/hr$
ATQ,
Radius $\left(r_1\right)$ of circular end of pipe $=\frac{Diameter}{2}$
$=\frac{20}{2}=10cm=0.1m$ $[1m=100cm]$
Similarly,
Radius $\left(r_2\right)$ of circular end of cylindrical tank $=\frac{10}{2}=5m$
Also,
Depth $\left(h_2\right)$ of cylindrical tank $=2m$
Now,
Area of cross-section $=\pi (r_1{)}^2=\pi \times (0.1{)}^2=0.01\pi$
Speed of water$=3km/h=\frac{3000}{60}=50m/min$.
Volume of water flowing in $1$ min from pipe $=50\times 0.01\pi =0.5\pi m^3.$
Volume of water flowing in ${}^{\prime }{t}^{\prime }$ minutes from pipe$=t\times 0.5\pi m^3$.
Therefore,
Volume of water flowing in ${}^{\prime }{t}^{\prime }$ minutes from pipe $=$ Volume of water in tank
$=t\times 0.5\pi m^3=\pi r^2{h}_2$
$=t\times 0.5=5^2\times 2$
$=t=100$ minutes.