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प्रश्न
Water is flowing through a cylindrical pipe of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m per second. Determine the rise in level of water in the tank in half an hour.
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उत्तर
We have,
the internal radius of the cylindrical pipe, r = 2/2 = 1 cm and
the base radius of cylindrical tank, R = 40 cm.
Also, the rate of flow, h = 0.4 m/s = 40 cm/s
Let the rise in level of water be H.
Now,
The volume of water flowing out of the cylindrical pipe in 1 sec =πr2h = π × 1 × 1 × 40 = 40π cm3
As,
Volume of water in the cylindrical tank = Volume of standing water in cylindrical pipe
⇒πR2H = 72000π
⇒R^2H = 72000`
⇒ 40 × 40 × H = 7200H
`rArr H = 72000/(40xx40)`
∴ H = 45 cm
So, the rise in level of water in the tank in half an hour is 45 cm.
Disclaimer: The answer given in the textbook is incorrect. The same has been corrected above.
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Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian pottery work which has attracted Indians as well as foreigners with a variety of tea sets, crockery and ceramic tile works. A huge portion of the ceramics used in the country is supplied by Khurja and is also referred as "The Ceramic Town". One of the private schools of Bulandshahr organised an Educational Tour for class 10 students to Khurja. Students were very excited about the trip. Following are the few pottery objects of Khurja.
Students found the shapes of the objects very interesting and they could easily relate them with mathematical shapes viz sphere, hemisphere, cylinder etc. |
Maths teacher who was accompanying the students asked the following questions:
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- If in the cylindrical jar full of water, a conical funnel of the same height and same diameter is immersed, then how much water will flow out of the jar?
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