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A hollow sphere of internal and external radii 2 cm and 4 cm respectively is melted into a cone of base radius 4 cm. Find the height and slant height of the cone.

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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 height and slant height of the cone
given that,
A hollow sphere of internal and external radii 2 cm
and 4 cm respectively is melted into a cone of base
radius 4 cm.

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1 Answer

  1. Given,

    The internal radius of hollow sphere = 2 cm

    The external radius of hollow sphere = 4 cm

    We know that,

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

    Also given,

    The base 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

    Now,

    Slant height of the cone (l) is given by

    l = √(h2 + r2)

    l = √(142 + 42) = √212

    l = 14.56 cm

    Therefore, the height and slant height of the conical heap are 14 cm and 14.56 cm respectively.

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