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
Deepak BoraNewbie
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