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Question
A farmer connects a pipe of internal diameter 25 cm from a canal into a cylindrical tank in his field, which is 12 m in diameter and 2.5 m deep. If water flows through the pipe at the rate of 3.6 km/hr, then in how much time will the tank be filled? Also, find the cost of water if the canal department charges at the rate of ₹ 0.07 per m3.
Solution
we have,
the radius of the cylindrical tank, R = `12/2` = 6m = 600 cm,
the depth of the tank, H = 2.5 m = 250 cm,
the radius of the cylindrical pipe, r = `25/2` = 12.5 cm,
speed of the flowing water, h = 3.6 Km/ h `="360000 m"/"3600 s" = 100 "cm"//s`
Now,
Volume of water flowing out from the pipe in a hour = πr2h
`=22/7xx12.5xx12.5xx100 "cm"^3`
Also,
Volume of the tank = πR2H
`=22/7xx600xx600xx250 "cm"^3`
So, the time taken to fill the tank`= "Volume of the tank"/"Volume of water flowing out from the pipe"`
`= ((22/7)xx600xx600xx250)/(22/7xx12.5xx12.5xx100)`
=5760 s
`=5760/3600`
= 1.6 h
Also, the cost pof water `=0.07xx22/7xx6xx6xx2.5`
= `₹19.80`
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Assertion (A)
If the radii of the circular ends of a bucket 24 cm high are 15 cm and 5 cm, respectively, then the surface area of the bucket is 545π cm2.
- Reason(R)
If the radii of the circular ends of the frustum of a cone are R and r, respectively, and its height is h, then its surface area is - Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
- Assertion (A) is true and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
