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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/H, in How Much Time Will the Tank Be Filled? - Mathematics

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/h, in how much time will the tank be filled?

 
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Solution

The internal radius of the pipe is 10 cm=0.1 m. The water is flowing in the pipe at 3km/hr = 3000m/hr.

Let the cylindrical tank will be filled in t hours. Therefore, the length of the flowing water in t hours is = 3000 x t meter

Therefore, the volume of the flowing water is V1= π x (0.1)2 x 3000 x t m3

The radius of the cylindrical tank is 5 m and the height is 2 m. Therefore, the volume of the cylindrical tank is

V=  π x (5)2 x 2 m3

Since, we have considered that the tank will be filled in t hours; therefore the volume of

the flowing water in t hours is same as the volume of the cylindrical tank. Hence, we have

V1 = V2

⇒`pixx(5)^2=pixx(0.1)^2xx3000xxt`

⇒`t=((5)^2xx2)/((0.1)^2xx3000)`

⇒`t=3/5`hours

`t=(5xx60)/3=100` minutes

Hence, the tank will be filled in 1 hour 40 minutes

 

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Exercise 14.1 | Q 51 | Page 30
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