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Question
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km per hour, in how much time will the tank be filled completely?
Solution
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 xx 1000 "m")/60` = 50 m
Volume of water flowing through pipe in 't' minutes = volume of water in cylindrical tank
t × πr2h = πR2H
t = `("R"^2"H")/("r"^2"h")`
= `(5 "m" xx 5 "m" xx 2 "m") / (0.1 "m" xx 0.1 "m" xx 50 "m")`
= 100
Therefore, the cylindrical tank will be filled in 100 minutes.
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