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What length of a solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of length 16 cm, external diameter 20 cm and thickness 2.5 mm?

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Very important question for board exam class 10. This question is from rd sharma class 10 from the mensuration chapter ecercise 16.1.

In this question  we have to find the length of a solid cylinder.

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  1. Diameter of the solid cylinder = 2 cm

     

    Length of hollow cylinder = 16 cm

     

    The solid cylinder is recast into a hollow cylinder of length 16 cm, external diameter of 20 cm and thickness of 2.5 mm = 0.25 cm

     

    We know that,

     

    Volume of a cylinder = πr2h

     

    Radius of the solid cylinder = 1 cm

     

    So,

     

    Volume of the solid cylinder = π12h = πh cm3

     

    Let’s assume the length of the solid cylinder as h

     

    And,

     

    Volume of the hollow cylinder = πh(R2– r2)

     

    Thickness of the cylinder = (R – r)

     

    0.25 = 10 – r

     

    So, the internal radius of the cylinder is 9.75 cm

     

    Volume of the hollow cylinder = π × 16 (100 – 95.0625)

     

    Hence, it’s understood that

     

    Volume of the solid cylinder = volume of the hollow cylinder

     

    πh = π × 16(100 – 95.06)

     

    h = 79.04 cm

     

    Therefore, the length of the solid cylinder is 79.04 cm.

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