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Question
What length of a solid cylinder 2cm in diameter must be taken to recast into a hollow
cylinder of length 16cm, external diameter 20cm and thickness 2.5mm?
Solution
Given that diameter of solid cylinder = 2cm
Given that solid cylinder is recast to hollow cylinder Length of hollow cylinder =16cm
External diameter = 20cm
Thickness = 2.5mm= 0.25cm
Volume of solid cylinder=`pir^2h`
Radius of cylinder =1cm
So volume of solid cylinder=`pi(1)^ 2h` ...........(i)
Let length of solid cylinder be h
Volume of hollow cylinder=`pih(R^2-r^2)`
Thickness =R - r
0.25 = 10 - r
⇒ Internal radius= 9.75cm
So volume of hollow cylinder = π x 16(100 - 95.0625) .........(2)
Volume of solid cylinder is equal to volume of hollow cylinder.
(1)=(2)
Equating equations (1) and (2)
`pi(1)^2h=pixx16(100-95.06)`
`22/7(1)^2xxh=22/7xx16(4.94)`
h=79.04cm
∴Length of solid cylinder =79cm
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