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What Length of Solid Cylinder 2 Cm in Diameter Must Be Taken to Recast into a Hollow Cylinder of External Diameter 20 Cm, 0.25 Cm Thickand 15 Cm Long? - Mathematics

Sum

What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thickand 15 cm long?

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Solution

External diameter of hollow cylinder=20 cm 

Therefore , radius=10 cm 

Thickness =0.25 cm 

Hence, Internal radius=(10-0.25)=9.75 cm 

Length of cylinder (h)=15 cm 

`∴"volume "=pih(R^2-r^2)=pixx15(10^2-9.75^2)`

`=15pi(100-95.0625)cm^3`

`= 15pixx4.9375 cm^3`

Diameter = `2cm`

Therefore, radius (r)=1 cm 

Let h be the lenght

`"then, volume"= pir^2h=pi(1xx1)h=pih`

Now, according to given condition: 

`pih=15pixx4.9375`

`⇒ h=15xx4.9375`

`⇒h=74.0625`

`"Length of cylinder" =74.0625 cm`

 

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