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Question
The radius of the internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively! If it is melted and recast into a solid cylinder of height `8/3` cm, find the diameter of the cylinder.
Solution
Internal radius of hollow spherical shell = r1 = 3 cm.
External radius of hollow spherical = r2 = 5 cm
Volume of hollow spherical = `4/3π(r_2^3 - r_1^3)`
= `4/3π[ (5)^3 - (3)^3]`
= `4/3` π (125 - 127)
= `(4π xx 98)/3`
= `(392π)/3` cm3
Volume of cylinder = πr2h
= πr2 x `8/3`
= `(8 πr^2)/3` cm3
Volume of cylinder = Volume of hallow sphere
`(8 πr^2)/3 = (392π)/3`
r2 = `(392π xx 3)/(8 π xx 3)`
r2 = 49
r = `sqrt49`
r = 7 cm.
The diameter of cylinder = 2r = 2 x 7 = 14 cm.
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