Question

A farmer connects a pipe of internal diameter 25 cm from a canal to a cylindrical tank in his field, which is 12 m in diameter and 2.5 m deep. If water flows through the pipe at the rate of 3.6 km/h, in how much time will the tank be filled? Also, find the cost of water if the canal department charges at the rate of Rs 0.07/m³.

Answer 1

Height of tank = 2.5 m
Diameter of tank = 12 m
Radius of tank = 6 m
Volume of the cylindrical tank$={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times 6\times 6\times 2.5=282.857{\mathrm{m}}^3$

Rate of flow $=3.6\raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$hr$}\right.=\frac{3.6\times 1000}{60\times 60}\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.=1\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Internal diameter of the pipe = 25 cm
Internal radius of the pipe = 12.5 cm = 0.125 m

Quantity of water flowing through the pipe in 1 sec$=\frac{22}{7}\times 0.125\times 0.125\times 1=0.049m^3$
Time taken to fill the tank$=\frac{282.857}{0.049}=5772.6seconds\approx 1hourand36minutes$

Cost of water is Rs 0.07/m³.
Thus, cost of filling the tank$=Rs282.857\times 0.07=Rs19.7999\approx Rs19.80$