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प्रश्न
A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.
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उत्तर
A cone has been reshaped in the sphere
Height of cone is 24 cm and the radius of the base is 6 cm
Volume of sphere = volume of cone
Volume of cone = `1/3`πr2h
Plugging the values in the formula we get
volume of cone = `1/3`π(6)224 = 288π cm3
Let the radius of sphere be r
Volume of sphere = `4/3`πr3
Since, the volume of cone = volume of sphere
Volume of sphere = 288π cm3
So,
288π = `4/3` πr3
⇒ 288 = `4/3`r3
⇒ r3 = 216
⇒ r = 6 cm
Hence, radius of reshaped sphere is 6 cm
Now, surface area of sphere = 4πr2
= 4π(6)2
= `144 × 22/7`
= 452.5 cm2
Therefore, surface area of sphere is 452.57 cm2
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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?
