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प्रश्न
The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is:
पर्याय
3
5
4
6
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उत्तर
Let r and h be the radius and the height of the cylinder, respectively.
Given:
Diameter of the cylinder = 4 cm
∴ Radius of the cylinder, r = 2 cm
Height of the cylinder, h = 45 cm
Volume of the solid cylinder = `pir^2h=pixx(2)^2xx45 cm^2=180pi cm^3`
Suppose the radius of each sphere be R cm.
Diameter of the sphere = 6 cm
∴ Radius of the sphere, R = 3 cm
Let n be the number of solids formed by melting the solid metallic cylinder.
∴ n × Volume of the solid spheres = Volume of the solid cylinder
`=>nxx4/3 pi R^3=180pi`
`=>nxx4/3 pi(3)^3=180pi`
`=>n=(180xx3)/(4xx27)=5`
Thus, the number of solid spheres that can be formed is 5.
Hence, the correct option is B.
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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?
Statement A (Assertion): Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.
Statement R( Reason): Top is obtained by joining the plane surfaces of the hemisphere and cone together.
