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

# 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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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