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Question
Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
Solution
Radius of metallic sphere = `2 mm = 1/5 cm`
Volume = `4/3pir^3`
= `4/3 xx 22/7 xx 1/5 xx 1/5 xx 1/5`
= `88/(21 xx 125) cm^3`
Volume of 8 spheres = `(88 xx 8)/(21 xx 125)`
= `704/(21 xx 125) cm^3` ...(1)
Let radius of new sphere = R
∴ Volume = `4/3piR^3`
= `4/3 xx 22/7R^3`
= `88/21R^3` ...(2)
From (1) and (2)
`88/21R^3 = 704/(21 xx 125)`
`=> R^3 = 704/(21 xx 125) xx 21/88 = 8/125`
`=> R = 2/5 = 0.4 cm = 4 mm`
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