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  • A farmer connects a pipe of internal diameter 20 cm from a 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?

A farmer connects a pipe of internal diameter 20 cm from a 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?

 

 

Answers (1)

Given \rightarrow diameter of tank = 10 m
             radius of tank, R = 5 m
             height of tank , H = 2 m
diameter of pipe = 20 cm

radius of pipe , r = 10 cm = \frac{10}{100}m
speed of water through pipe, = 3km/hr = \frac{3000}{60\times 60}\, m/s
Solution \rightarrow volume of tank = volume of water through pipe
                    \pi R^{2}H= \pi \times r^{2}\times \vartheta \times t   (vt = length per unit time) 
\Rightarrow 5^{2}\times 2= \left ( \frac{10}{100} \right )^{2}\times \frac{3000}{60\times 60}\times t
\Rightarrow 50= \frac{1}{100}\times \frac{30}{6\times 6}\times t
\Rightarrow \frac{50\times 10\times 6\times 6}{3}= t
\Rightarrow t= 6000\, seconds
\Rightarrow t= 100\, minutes\, \left ( \frac{6000}{60}\, minutes \right )
time taken to fill the tank = 100 minutes

Posted by

Safeer PP

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