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Ex 13.3, 2 - Metallic spheres of radii 6 cm, 8 cm and 10 cm - Ex 13.3

  1. Chapter 13 Class 10 Surface Areas and Volumes
  2. Serial order wise
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Ex 13.3, 2 Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere. Since 3 spheres are melted to from one new sphere. Volume of 3 old sphere = volume of new sphere Volume of 1st sphere + volume of 2nd sphere + volume of 3rd sphere = Volume of new sphere Volume of 1st sphere, Radius (r1) = 6 cm Volume of 1st sphere = 4/3 ๐œ‹(๐‘Ÿ1)3 = 4/3ร—๐œ‹ร—(6)^3 = 4/3ร—๐œ‹ร—216 Volume of 2nd sphere, Radius (r2) = 8 cm Volume of 2nd sphere = 4/3 ๐œ‹(๐‘Ÿ2)3 = 4/3ร—๐œ‹ร—(8)^3 = 4/3ร—๐œ‹ร—512 Volume of 3rd sphere, Radius (r3) = 10 cm Volume of 1st sphere = 4/3 ๐œ‹(๐‘Ÿ3)3 = 4/3ร—๐œ‹ร—(10)^3 = 4/3ร—๐œ‹ร—1000 Volume of new sphere Let Radius = r cm Volume of new sphere = 4/3 ฯ€๐‘Ÿ^3 Now , Volume of new sphere = Volume of (1st + 2nd + 3rd ) spheres 4/3 ๐œ‹๐‘Ÿ3 = 4/3 ๐œ‹ร—216+4/3 ๐œ‹ร—512+4/3 ๐œ‹ร—1000 4/3 ๐œ‹๐‘Ÿ3 = 4/3 ๐œ‹ (216 + 512 + 1000) 4/3 ๐œ‹๐‘Ÿ3 = 4/3 ๐œ‹ (1728) r3 = 1728 r = โˆ›1728 r = โˆ›(12ร—12ร—12) r = โˆ›((12)3) r = 12 cm Hence, radius of the resulting sphere = 12 cm

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