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प्रश्न
A bucket has top and bottom diameter of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm2 . (Use π = 3.14)
उत्तर
The radii of the top and bottom circles are r1 = 20 cm and r2 = 10 cm respectively. The height of the bucket is h= 12 cm. Therefore, the volume of the bucket is
`V=1/3pi(r_1^2+r_1r_2+r_2^2)xxh`
`=1/3pi(20^2+20xx10+10^2)xx12`
`=1/3xx22/7xx700xx12`
= 8800 cm3
The slant height of the bucket is
`l=sqrt((r_1-r_2)^2+h^2)`
`=sqrt((20+10)^2+12^2)`
`=sqrt(244)`
`=2sqrt(61) cm`
The total surface area of the bucket is
`=pi(r_1-r_2)xxl+pir_2^2`
`=22/7xx(20+10)xx2sqrt(61)+22/7xx10^2`
`=(1320sqrt(61)+2200)/7xxcm^2`
`=(1320sqrt(61)+2200)/7xx100 dm^2`
The total cost of tin sheet used for making the bucket is
`=1.20xx((1320sqrt(61)+2200)/(7xx100))`
= 21.40
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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?
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.
