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A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42 cm and height 21 cm which are filled completely. Find the diameter of the cylindrical vessel?

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This question is from mensuration chapter of rd sharma Class 10, chapter 16 .

I need solution of this question . In this question we have to find diameter of cylindrical vessel.

A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42 cm and height 21 cm which are filled completely.

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  1. The diameter of the cylinder = the height of the cylinder

     

    ⇒ h = 2r, where h – height of the cylinder and r – radius of the cylinder

     

    We know that,

     

    Volume of a cylinder = πr2h

     

    So, volume of the cylindrical vessel = πr22r = 2πr3 (as h = 2r)….. (i)

     

    Now,

     

    Volume of each identical vessel = πr2h

     

    Diameter = 42 cm, so the radius = 21 cm

     

    Height = 21 cm

     

    So, the volume of two identical vessels = 2 x π 212 × 21 ….. (ii)

     

    Since the volumes on equation (i) and (ii) are equal

     

    On equating both the equations, we have

     

    2πr3= 2 x π 212 × 21

     

    r3 = (21)3

     

    r = 21 cm

     

    So, d = 42 cm

     

    Therefore, the diameter of t he cylindrical vessel is 42 cm

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