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Deepak Bora
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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 =  [4/3] π [ R³ – r³]

    = [4/3] π [ 12³ – 9³]

    = [4/3] π [ 1728 – 729]

    = [4/3] π × (999)

    = 4 × π ×(333) cm³

    Height of cylinder = 37 cm

    radius of cylinder be r cm.

    Volume of cylinder = πr²h

    = πr²37

    Volume of the shell = Volume of cylinder

    4π ×(333) = πr²37

    r² = [4 ×(333)] / 37

    r = √4 ×9

    = √36

    = 6 cm

    diameter of the base of the cylinder

    = 2r

    = 12 cm.

    ∴ diameter of the base of the cylinder is 12cm

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