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प्रश्न
Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?
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उत्तर
Given:-
Speed of flowing water = 4km/h = 200/3 metres per minute
Width of canal = 6 m and height of canal = 1.5 m
Standing water requirement for irrigation = 8 cm = 0.08 m
Cross section area of canal = width of canal x height of canal = (6 * 1.5) m2
Volume of water needed to irrigate in 10 min = 10 x 6 x 1.5 x 200/3 = 6000m3
Volume of water irrigated = base area (of irrigated land) x height
= base area x 0.08m
6000 = base area x 0.08
Base area = 6000/0.08 =75000 m2
= 7.5 hectare [1 hectare = 10000 m2]
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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:
- The internal radius of hemispherical bowl (filled completely with water) in I is 9 cm and the radius and height of the cylindrical jar in II are 1.5 cm and 4 cm respectively. If the hemispherical bowl is to be emptied in cylindrical jars, then how many cylindrical jars are required?
- 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?
