Math, asked by BrainlyHelper, 1 year ago

Water is flowing at the rate of 2.52\frac{km}{h} through a cylindrical pipe into a cylindrical tank, the radius of the base is 40 cm. If the increase in the level of water in the tank, in half an hour is 3.15 m, find the internal diameter of the pipe.

Answers

Answered by nikitasingh79
11

Answer:

The internal diameter of the pipe is 4 cm.

Step-by-step explanation:

Let the internal Radius of the cylindrical pipe be r.

Given :  

In half an hour Increase in the level of water, h = 3.15 m =  3.15 × 100 = 315 cm

[1 m = 100 cm]

Radius of the water tank, r = 40 cm

Volume of water that falls in the cylindrical tank in half an hour = πr²h

=  π x (40)² x 315  = π × 1600 × 315  

Volume of water that falls in the cylindrical tank in half an hour = 5,04,000 π cm³

Water is flowing at the rate of = 2.52 km/h

Length of water flowing  in half an hour , H  =  2.52 × 30 / 60  = 2.52 /2 = 1.26 km = 1.26 × 100000 = 1,26,000 cm

[1 km = 100000 cm]

Volume of the water that flows through the pipe in half an hour = πr²H =   π x (r)² x 126000 cm³

Volume of the water that flows through the pipe in half an hour = Volume of water that falls in the cylindrical tank in half an hour

π x (r)² x 126000  = 504000π

(r)² x 126000  = 504000

r² = 504000/ 126000

r² = 4

r = √4

r = 2

Diameter (d) = 2r  

d = 2 × 2  

d = 4 cm

Hence,the internal diameter of the pipe is 4 cm.

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Answered by ROCKSTARgirl
5

Answer:

The internal diameter of the pipe is 4 cm.

Step-by-step explanation:

Let the internal Radius of the cylindrical pipe be r.

Given :  

In half an hour Increase in the level of water, h = 3.15 m =  3.15 × 100 = 315 cm

[1 m = 100 cm]

Radius of the water tank, r = 40 cm

Volume of water that falls in the cylindrical tank in half an hour = πr²h

=  π x (40)² x 315  = π × 1600 × 315  

Volume of water that falls in the cylindrical tank in half an hour = 5,04,000 π cm³

Water is flowing at the rate of = 2.52 km/h

Length of water flowing  in half an hour , H  =  2.52 × 30 / 60  = 2.52 /2 = 1.26 km = 1.26 × 100000 = 1,26,000 cm

[1 km = 100000 cm]

Volume of the water that flows through the pipe in half an hour = πr²H =   π x (r)² x 126000 cm³

Volume of the water that flows through the pipe in half an hour = Volume of water that falls in the cylindrical tank in half an hour

π x (r)² x 126000  = 504000π

(r)² x 126000  = 504000

r² = 504000/ 126000

r² = 4

r = √4

r = 2

Diameter (d) = 2r  

d = 2 × 2  

d = 4 cm

Hence,the internal diameter of the pipe is 4 cm.


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