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A spherical shell of lead, whose external and internal diameters are 24 cm and 18 cm, is melted and recast into a right circular cylinder 37 cm high. Find the diameter of the base of the cylinder

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This problem is the shell problem. Problem from RS Aggarwal book, problem number 12, page number 810, exercise 17B, chapter volume and surface area of solid.
Chapter Mensuration

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1. Given data,

External diameter of the shell = 24 cm

External radius of the shell = R = 12 cm

Internal diameter of the shell = 18 cm

Internal radius of the shell = r = 9 cm

Volume of the shell = Â [4/3] Ï€ [ RÂ³ â€“ rÂ³]

= [4/3] Ï€ [ 12Â³ â€“ 9Â³]

= [4/3] Ï€ [ 1728 â€“ 729]

= [4/3] Ï€ Ã— (999)

= 4 Ã— Ï€ Ã—(333) cmÂ³

Height of cylinder = 37 cm

radius of cylinder be r cm.

Volume of cylinder = Ï€rÂ²h

= Ï€rÂ²37

Volume of the shell = Volume of cylinder

4Ï€ Ã—(333) = Ï€rÂ²37

rÂ² = [4 Ã—(333)] / 37

r = âˆš4 Ã—9

= âˆš36

= 6 cm

diameter of the base of the cylinder

= 2r

= 12 cm.

âˆ´ diameter of the base of the cylinder is 12cm

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