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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? - Mathematics

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?

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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.


Equating equations (1) and (2)




∴Length of solid cylinder =79cm





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RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Exercise 14.1 | Q 5 | Page 28
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