# Water Flows Out Through a Circular Pipe Whose Internal Diameter is 2 Cm, at the Rate of 6 Metres per Second into a Cylindrical Tank. the Radius of Whose Base is 60 Cm. - Mathematics

Sum

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank. The radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?

#### Solution

Given data is as follows:

Internal diameter of the pipe = 2 cm

Water flow rate through the pipe = 6 m/sec

Radius of the tank = 60 cm

Time = 30 minutes

The volume of water that flows for 1 sec through the pipe at the rate of 6 m/sec is nothing but the volume of the cylinder with h = 6.

Also, given is the diameter which is 2 cm. Therefore,

r = 1 cm

Since the speed with which water flows through the pipe is in meters/second, let us convert the radius of the pipe from centimeters to meters. Therefore,

 r = 1/100  m

Volume of water that flows for 1 sec = 22/7 xx 1/100 xx 1/100 xx 6

Now, we have to find the volume of water that flows for 30 minutes.

Since speed of water is in meters/second, let us convert 30 minutes into seconds. It will be 30 × 60

Volume of water that flows for 30 minutes = 22/7 xx 1/100 xx 1/100 xx 6 xx 30 xx 60

Now, considering the tank, we have been given the radius of tank in centimeters. Let us first convert it into meters. Let radius of tank be ‘R’.

R= 60 cm

R=60/100

Volume of water collected in the tank after 30 minutes= 22/7 xx 60/100 xx 60/100 xx h

We know that,

Volume of water collected in the tank after 30 minutes= Volume of water that flows through the pipe for 30 minutes

22/7 xx 60/100 xx 60/100 xx h = 22/7 xx 1/100 xx 1/100 xx 6 xx 30 xx 60

h = 3 m

Therefore, the height of the tank is 3 meters.

Concept: Surface Area of Cylinder
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 19 Surface Areas and Volume of a Circular Cylinder
Exercise 19.2 | Q 29 | Page 22

Share