Question

Water is flowing at the rate of 3km/hr through a circular pipe of 20cm internal diameter into a cylindrical tank of diameter 10m. and depth 2m. In how much time will the cistern be filled ?​

Answer 1

Answer:

Suppose the cistern is filled in x hours. Since water is flowing at the rate of 3km/hr.

Therefore length of the water column in x hours =3x km =3000x metres

Clearly, the water column forms a cylinder of radius

r=

2

20

cm=10cm=

10

1

m and h= height =3000x metres

Volume of the water that flows in the cistern in x hours

=πr

2

h=(

7

22

×

10

1

×

10

1

×3000x)m

3

Also volume of the cister =(

7

22

×5×5×2)m

3

Since the cistern is filled in x hours

Volume of the water that flows in the cistern in x hours = volume of the cistern

⇒

7

22

×

10

1

×

10

1

×3000x=

7

22

×5×5×2

⇒x=(

3000

5×5×2×10×10

)hrs=1hour40minutes

∴ Cistern is filled in 1hour40minutes

Answer 2

Hint:

• In this question time taken to fill the cistern will be the ratio of volume of cistern and the volume of water coming out of the pipe in one hour, and we know that volume of the cylinder is given as

$\\ \\ \\ \pi {r}^{2} h$

Complete step-by-step answer:

The cistern is in cylindrical shape

Volume of a cylinder =

$\\ \pi {r}^{2} h$

$\\ \\ \\ \\ Radius \: \: \: of \: \: \: cristern \: = \frac{10}{2} \\ = 5m$

Hence volume of the cristern

$\\ \\ \\ \\ \pi \times 5 \times 5 \times 2 \: \: {m}^{3}$

Radius of pipe -

$\\ \\ \\ \frac{20 }{2 \times 100} = \frac{1}{10} \: m$

Since the pipe is cylindrical in shape,

Since the pipe is cylindrical in shape,Volume =

$\\ \\ \\ \pi {r}^{2} h$

Here, height is considered as the distance traveled = 3km=3000m

Hence, volume of water coming out of pipe in one hour =

$\\ \\ \\ \\ \pi \times( { \frac{1}{10} )}^{2} \times 3000 \: \: {m}^{3}$

Now time taken to fill the cristern -

$\\ \\ \\ = \frac{Volume \: \: of \: \: the \: \: cristern}{Volume \: of \: wate r\: coming \: out \:o f \:pipe \: in \: 1h our} \\ \\ \\ \\ = \frac{\pi \times 5 \times 5 \times 2}{\pi \times \frac{1}{10} \times \frac{1}{10} \times 3000 } \\ \\ \\ \\ \\ = \frac{5}{3} hrs \\ \\ \\ \\ \\ = 1 \: hour \: + \: \frac{2}{3} hour \\ \\ \\ \\ \\ \\ = 1hour \: 40 \: minutes$

NOTE:

• In order to solve these types of problems, first of all remember the formula of all the shapes. Second the height of the pipe is given as the rate of flowing water which we treated as height to solve the problem. Because the amount of water flowing through the pipe in one hour is given as km/ hr. So, if we consider it for one hour the water forms a circular cylinder of radius 10 cm and height 3000m for the above problem. So taking this logic we solved the above problem.