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
Question:

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 the 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 $\tan k=\pi r^{2} h$

= 22/7 × 0.7 × 0.7 × 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 into metres. It then becomes, 3.5/200 m.

Volume of water that flows through the pipe in 1 second = 22/7 × 3.5/200 × 3.5/200 × 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 × 3.5/200 × 3.5/200 × 2 × x

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 × 3.5/200 × 3.5/200 × 2 × x = 22/7 × 0.7 × 0.7 × 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.

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