Question

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

Answer 1

Radius of the cylinder = $\frac{10}{2}$ = 5 m

Depth = Height = 2 m

Volume of cylindrical tank = $\pi$$r^{2}h$

= $\pi$ $\times$ $5^2\times 2$ = 50$\pi$ $m^3$

Radius of the pipe = $\frac{20}{2}$ = 10 cm = 0.1 m

Length of the pipe = 3000 m

Now, volume of the water that flow through pipe in 1 hour = $\pi$$r^{2}l$ [ Here, h =l]

= $\pi$ $\times$ ${0.1}^2\times 3000$ = 30 $\pi$ $m^3$

Now, volume of the water that flow through pipe in 't' hours = 30 $\pi$ $\times$ t $m^3$

volume of the water that flow through pipe in 't' hours

30 $\pi$ $\times$ t $m^3$ = 50$\pi$ $m^3$

$\Rightarrow$ t = $\frac{50}{30}$

$\Rightarrow$ t = $\frac{5}{3}$ hrs

$\Rightarrow$ t = $\frac{5}{3}$ $\times$ 60 mins = 100 mins