Question

The radius of a cylindrical cistern is 10 m and its
height is 15 cm. It is filled with water through a pipe
whose diameter is 50 cm water is flowing out of the
with a velocity 5m/sec. How many minutes will it take
in filling the cistern with water?​

Answer 1

Answer:

★ In 80 minutes ★

Step-by-step explanation:

Given:

• Radius of cylindrical cistern is 10m
• Height is 15 m
• Diameter of pipe is 50 cm
• Water is flowing at velocity of 5m/sec

To Find:

• In how many minutes cistern will fill with water.

Solution: We know that

★ Volume of cylinder= πr²h ★

∴ Volume of cylindrical cistern = π x (10)² x 15

$\small\implies{\sf }$ Volume = π x 10 x 10 x 15

† Radius of pipe =

$\small\implies{\sf }$ Diameter/2 = 50/2 = 25cm or 25/100m

Since, The pipe is cylindrical in shape

∴ Volume of pipe = πr²h

• Here, Height is considered as the Distance travelled

Therefore, Volume of water coming from pipe in one second = πr²h

$\small\implies{\sf }$ π x (25/100)² x 5m

$\small\implies{\sf }$ Volume = π x 25/100 x 25/100 x 5

Now, The time taken to fill the cistern=

• Volume of cistern / Volume of water coming from pipe in one second

$\small\implies{\sf }$ π x 10 x 10 x 15 / π x 25/100 x 25/100 x 5

$\small\implies{\sf }$ π x 1500 x 100 x 100 / π x 3125

$\small\implies{\sf }$ 15000000π / 3125π

$\small\implies{\sf }$ 4800 Seconds

★ Changing in hours = 4800/60 = 80 minutes

Hence, in 80 minutes the cistern will fill with water

Answer 2

Answer:

Given:

Radius is 10m

Height is 15 m

Diameter is 50 cm

Water is flowing at velocity of 5m/sec

To Find:

In how many minutes cistern will fill with water.

Solution:

We know that

Volume of cylinder= πr²h

∴Volume of cylindrical cistern = π x (10)² x 15

⟹ Volume = π x 10 x 10 x 15

† Radius of pipe =

⟹ Diameter/2 = 50/2 = 25cm or 25/100m

Since, The pipe is cylindrical in shape

∴ Volume of pipe = πr²h

• Here, Height is considered as the Distance travelled

Therefore, Volume of water coming from pipe in one second = πr²h

π x (25/100)² x 5m

Volume = π x 25/100 x 25/100 x 5

Now, The time taken to fill the cistern=

Volume of cistern / Volume of water coming from pipe in one second

π x 10 x 10 x 15 / π x 25/100 x 25/100 x 5

π x 1500 x 100 x 100 / π x 3125

15000000π / 3125π

4800 Seconds

Changing in hours = 4800/60 = 80 minutes

Hence, in 80 minutes the cistern will fill with water

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