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Question
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.
Solution
External diameter of the shell = 24 cm
External radius of the shell = 12 cm
Internal diameter of the shell = 18 cm
Internal radius of the shell = 9 cm
Volume of the
`"shell" = 4/3pi (12^3 -9^3) =4/3pi(1728 - 729)=4/3pixx(999)=4pi xx (333) "cm"^3`
Height of cylinder = 37 cm
Let radius of cylinder be r cm.
Volume of cylinder =`pir^2h = 37pir^2 "cm"^3`
Volume of the shell = Volume of cylinder
Or, 4π ×(333)= 37πr2
`⇒ r^2=(4xx333)/37 = 4xx9`
`rArr r =sqrt(4xx9)=sqrt(36) = 6 "cm"`
So, diameter of the base of the cylinder = 2r = 12 cm.
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