Question

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

• A. 80
• B. 100
• C. 150
• D. 200

Answer 1

Answer: (A), (B)

The correct options are
A

80

B

100

Let cylindrical tank be filled in x hours
Diameter of pipe = d =20 cm

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

Speed of water flowing through pipe = 3 km/h = 3000 m/h

Volume of water flowing through pipe in 1 hour = $\pi .r^2.h=\pi \times 0.1\times 0.1\times 3000=30\pi m^3$

Volume of water flowing through pipe in x hours =30x.$\pi m^3$

Diameter of cylindrical tank = $d_1=10m$

Radius of cylindrical tank = $r_1=\frac{10}{2}=5m$

Height of cylindrical tank = $h_1=2m$

Volume of cylindrical tank = $\pi .(r_1{)}^2.h_1=\pi \times 5\times 5\times 2=50\pi m^3$
According to given condition we have:

Volume of water flowing through pipe in x hours = Volume of cylindrical tank

$\Rightarrow$ 30x.$\pi$ =50$\pi$

$x=\frac{50}{30}=\frac{5}{3}hours=100minutes$