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A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Calculate the height of the cone?

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Rd sharma class 10 maths exercise-16.1 mensuration.

In this question we have to calculate the height of the
cone given that a hollow sphere of internal and external
diameters 4 cm and 8 cm respectively is melted into a
cone of base diameter 8 cm.

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1 Answer

  1. Given,

    Internal diameter of hollow sphere = 4 cm

    So, the internal radius of hollow sphere = 2 cm

    External diameter of hollow sphere = 8 cm

    So, the external radius of hollow sphere = 4 cm

    We know that,

    Volume of the hollow sphere 4/3 π × (43 – 23) … (i)

    Also given,

    Diameter of the cone = 8 cm

    So, the radius of the cone = 4 cm

    Let the height of the cone be x cm

    Volume of the cone 1/3 π × 42 × h ….. (ii)

    As the volume of the hollow sphere and cone are equal. We can equate equations (i) and (ii)

    So, we get

    4/3 π × (43 – 23) = 1/3 π × 42 × h

    4 x (64 – 8) = 16 x h

    h = 14

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