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The diameters of internal and external surfaces of a hollow spherical shell are 10cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of 8/3, find the diameter of the cyli nder?

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This question is from r d sharma class 10 maths.

I found this question while doing maths class 10. I need help in getting the solution.

In this question we have to find the diameter of the cylinder given that the diameters of internal and external surfaces of a hollow spherical shell are 10cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of 8/3.

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1 Answer

  1. Given,

    Internal diameter of the hollow sphere = 6 cm

    So, the internal radius of the hollow sphere = 6/2 cm = 3 cm = r

    External diameter of the hollow sphere = 10 cm

    So, the external radius of the hollow sphere = 10/2 cm = 5 cm = R

    We know that,

    Volume of the hollow spherical shell = 4/3 π × (R3 – r3)

    = 4/3 π × (53 – 33) ….. (i)

    And given, the length of the solid cylinder = 8/3 cm

    Let the radius of the solid cylinder be r cm

    We know that,

    Volume of the cylinder = π × r2 × h

    = π × r2 × 8/3 ….. (ii)

    Now equating both (i) and (ii), we have

    4/3 π × 53 – 33 = π × r2 × 8/3

    4/3 x (125 – 27) = r2 × 8/3

    98/2 = r2

    r2 = 49

    r = 7

    So, d = 7 x 2 = 14 cm

    Therefore, the diameter of the cylinder is 14 cm

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