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Question
A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of the copper be 8.8 g per cm3, then find the weight of the wire.
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Solution
We have,
Diameter of the coppe wire, d = 6 mm = 0.6 cm,
Radius of the copper wire, `r = 0.6/2 = 0.3 "cm",`
Length of the cylinder, H = 18 cm,
Radius of the cylinder, `"R" =49/2`
The Number of rotations of the wire on the cylinder`= "Length of the cylinder, H"/ "Diameter of the copper wire, d"`
`= 18/0.6`
= 30
The circumferences of the base of the cylinder `= 2piR = 2xx22/7xx49/2 = 154 "cm"`
So, the of the wire, h = 30 × 154 = 4620 cm = 46.2 m
Now, The volume of the wire = πR2
`= 22/7xx0.3xx0.3xx4620`
= 1306.8 cm3
Also, the weigt of the = Volume of the wire × Density of the wire
= 1306.8 × 8.8
= 11499.84 g
≈ 11.5 Kg
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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?
The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends.
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A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 3 m and 14 m respectively, and the total height of the tent is 13.5 m, find the area of the canvas required for making the tent, keeping a provision of 26 m2 of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of ₹ 500 per m2.
