Water is flowing at the rate of 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
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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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.