A farmer connects a pipe of internal diameter 20 cm from 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:
A figure is drawn to visualize the shapes according to the given question.
From the above figure, it can be seen that the shape of the cross-section of the pipe is cylindrical. So, the volume of the water, flowing at the speed of 3 km/h through the pipe to fill the tank will be the same as the volume of water in the cylindrical tank.
To find the volume of the water we need to find the length of the water flowing through the pipe at the speed of 3 km/h.
Let us find the volume of the water by using the formula;
Volume of the cylinder = πr2h, where r and h are the radius and height of the cylinder respectively.
Therefore, the volume of water flowing through the pipe = volume of water in the cylindrical tank.
Radius of the cylindrical tank, R = 10 / 2 m = 5 m
Depth of the cylindrical tank, H = 2 m
Radius of the cylindrical pipe, r = 20/2 cm = 10/100 m = 0.1 m
Length of the water flowing through the pipe in 1 hour (60 minutes) = 3 km
Length of the water flowing through the pipe in 1 minute, h = 3 km/60 = (3 × 1000 m) /60 = 50 m
Volume of water flowing through pipe in 't' minutes = volume of water in cylindrical tank
t × πr2h = πR2H
t = R2H / r2h
= (5 m × 5 m × 2 m) / (0.1 m × 0.1 m × 50 m)
= 100
Therefore, the cylindrical tank will be filled in 100 minutes.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 13
Video Solution:
A farmer connects a pipe of internal diameter 20 cm from 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?
NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.3 Question 9
Summary:
If a farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep, and if water flows through the pipe at the rate of 3 km/h, the time taken to fill the tank will be 100 minutes.
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