A small container is made from length of a metal tube of external radius 10cm, the pipe is 2cm thick ,by wielding on to one disc of the same metal 1cm thick and 10cm in radius .if the length of compelete container is 6cm ,find the volume of metal in it
 

Dear Student,

Please find below the solution to the asked query:

Given  : A small container is made from length of a metal tube of external radius = R = 10 cm, the pipe is 2 cm thick , So

Internal radius  r  =  10 - 2 =   8 cm 

And

By wielding on to one disc of the same metal 1 cm thick and 10 cm in radius . , So

Height of cylindrical disc =  Thickness of disc  =  1 cm 

And

Radius of disc  =  10 cm

And

The length of complete container is 6 cm , So

Height of hollow metal tube = h =   6 -  1 ( Height of disc ) =   5  cm 

So,

The volume of metal in container  = Volume of hollow metal tube +  Volume of disc

We know : Volume of hollow cylinder  = $\mathrm{\pi }$ h ( R ² - r ²  )    and volume of cylinder  = $\mathrm{\pi }$  r ² h  , So

The volume of metal in container  = $\mathrm{\pi }$ ( 5 ) ( 10 ² - 8 ²  )  + $\mathrm{\pi }$ ( 10 )² ( 1 )

The volume of metal in container  = $\mathrm{\pi }$ ( 5 ) ( 100 - 64 )  + 100 $\mathrm{\pi }$

The volume of metal in container  = $\mathrm{\pi }$ ( 5 ) ( 36 )  + 100 $\mathrm{\pi }$

The volume of metal in container  = 180 $\mathrm{\pi }$  + 100 $\mathrm{\pi }$

The volume of metal in container  = 280 $\mathrm{\pi }$ 

The volume of metal in container  = 280 $\times \frac{22}{7}$ 

The volume of metal in container  = 40 $\times$ 22

The volume of metal in container  = 880 cm³                                                      (  Ans )

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