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Eight metallic spheres, each of radius 2 cm, are melted and cast into a single sphere. Calculate the radius of the new (single) sphere.

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ICSE Board Question Based on Mensuration Chapter of M.L Aggarwal for class10
In this question given that eight metallic spheres, each of radius 2 cm, are melted and cast into a single sphere. Calculate the radius of the new (single) sphere.
This is the Question Number 07, Exercise 17.5 of M.L Aggarwal.

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  1. Given radius of each sphere, r = 2 cm

    Volume of a sphere = (4/3)r3

    = (4/3)×23

    = (4/3)×8

    = (32/3) cm3

    Volume of 8 spheres = 8×(32/3)

    = (256/3) cm3

    Let R be radius of new sphere.

    Volume of the new sphere = (4/3)R3

    Since 8 spheres are melted and casted into a single sphere, volume remains same.

    (4/3)R3 = (256/3)

    4R3 = 256

    R3 = 256/4 = 64

    Taking cube root

    R = 4 cm

    Hence the radius of the new sphere is 4 cm.

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