Last updated at May 29, 2018 by Teachoo

Transcript

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(๐1)3 = 4/3ร๐ร(6)^3 = 4/3ร๐ร216 Volume of 2nd sphere, Radius (r2) = 8 cm Volume of 2nd sphere = 4/3 ๐(๐2)3 = 4/3ร๐ร(8)^3 = 4/3ร๐ร512 Volume of 3rd sphere, Radius (r3) = 10 cm Volume of 1st sphere = 4/3 ๐(๐3)3 = 4/3ร๐ร(10)^3 = 4/3ร๐ร1000 Volume of new sphere Let Radius = r cm Volume of new sphere = 4/3 ฯ๐^3 Now , Volume of new sphere = Volume of (1st + 2nd + 3rd ) spheres 4/3 ๐๐3 = 4/3 ๐ร216+4/3 ๐ร512+4/3 ๐ร1000 4/3 ๐๐3 = 4/3 ๐ (216 + 512 + 1000) 4/3 ๐๐3 = 4/3 ๐ (1728) r3 = 1728 r = โ1728 r = โ(12ร12ร12) r = โ((12)3) r = 12 cm Hence, radius of the resulting sphere = 12 cm

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.