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Ex 13.3, 1 - A metallic sphere of radius 4.2 cm is melted - Conversion of one shape to another

  1. Chapter 13 Class 10 Surface Areas and Volumes
  2. Serial order wise
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Ex 13.3, 1 A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder. Since sphere is melted into a cylinder , So, Volume of sphere = volume of cylinder Volume of sphere Radius = r = 4.2 cm volume of sphere = 4/3 ๐œ‹๐‘Ÿ3 = 4/3 ๐œ‹(4.2)3 Volume of cylinder Radius = r = 6 cm Let height = h cm Volume of cylinder = ๐œ‹๐‘Ÿ2โ„Ž = ๐œ‹ร—6^2ร—โ„Ž = 36๐œ‹h Now, Volume of sphere = Volume of cylinder 4/3 ๐œ‹(4.2)3= 36๐œ‹h 4/3 ๐œ‹(4.2)3ร—1/36๐œ‹ = h h = 4/3 ๐œ‹(4.2)3ร—1/36๐œ‹ h = 4/3ร—(4.2)3ร—1/36 h = 4/3ร—4.2ร—4.2ร—4.2ร—1/36 h = (4.2 ร— 4.2 ร— 4.2)/27 h = (4.2 ร— 4.2 ร— 4.2)/(3 ร— 3 ร— 3) h = 1.4 ร— 1.4 ร— 1.4 h = 2.744 cm Hence, height of cylinder = 2.744 cm

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