A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 metre per second. In how much time the tank will be filled?
Solution
Given data is as follows:
Diameter of the tank = 1.4 m
Height of the tank = 2.1 m
Diameter of the pipe = 3.5 cm
Water flow rate = 2 m/sec
We have to find the time required to fill the tank using this pipe.
The diameter of the tank is given which is 1.4 m. Let us find the radius.
r = `1.4/2`
=0.7 m
Volume of the tank = `pir^2h`
= `22/7 xx 0.7 xx 0.7 xx 2.1`
Given is the diameter of the pipe which is 3.5 cm. Therefore, radius is `3.5/2`cm. Let us convert it to meters. It then becomes, `3.5/200`m.
Volume of water that flows through the pipe in 1 second = `22/7 xx 3.5/200 xx 3.5/200 xx 2`
Let the time taken to fill the tank be x seconds. Then we have,
Volume of water that flows through the pipe in x seconds = `22/7 xx3.5/200 xx 3.5/200 xx 2xxx`
We know that volume of the water that flows through the pipe in x seconds will be equal to the volume of the tank. Therefore, we have
Volume of water that flows through the pipe in x seconds= Volume of the tank
`22/7 xx 3.5/200 xx3.5/200 xx 2 xx x= 22/7 xx 0.7 xx 0.7 xx 2.1`
x =1680 seconds
x=`1680/60` minutes
x =28 minutes
Hence, it takes 28 minutes to fill the tank using the given pipe.
