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A farmer connects a pipe of internal diameter 20 cm form a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled? - CBSE Class 10 - Mathematics

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Question

A farmer connects a pipe of internal diameter 20 cm form a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

Solution

Consider an area of cross-section of pipe as shown in the figure.

Radius (r1) of circular end of pipe = 20/200 = 0.1 m

Area of cross-section = `pixxr_1^2 = pixx(0.1)^2 = 0.01pi m^2`

Speed of water = 3 km/h = 3000/60 = 50 meter/min

Volume of water that flows in 1 minute from pipe = 50 × 0.01 π = 0.5π m3

Volume of water that flows in t minutes from pipe = t × 0.5π m3

Radius (r2) of circular end of cylindrical tank = 10/2 = 5m

Depth (h2) of cylindrical tank = 2 m

Let the tank be filled completely in t minutes.

Volume of water filled in tank in t minutes is equal to the volume of water flowed in t minutes from the pipe.

Volume of water that flows in t minutes from pipe = Volume of water in tank

t × 0.5π = π ×(r2)2 ×h2

t × 0.5 = 52 ×2

t = 100

Therefore, the cylindrical tank will be filled in 100 minutes.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 13: Surface Areas and Volumes
Ex. 13.30 | Q: 9 | Page no. 252

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Solution A farmer connects a pipe of internal diameter 20 cm form a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled? Concept: Conversion of Solid from One Shape to Another.
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