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Deepak Bora
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The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform cross-section. If the length of the wire is 36 m, find its radius.

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ICSE Board Question Based on Mensuration Chapter of M.L Aggarwal for class10
In this question diameter of a metallic sphere is given. The sphere is melted and drawn into a wire of uniform cross-section. If the length of the wire is also given then find its radius.
This is the Question Number 01, Exercise 17.5 of M.L Aggarwal.

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  1. Given diameter of the metallic sphere = 6 cm

    Radius of the sphere, r = 6/2 = 3 cm

    Volume of the sphere, V = (4/3)r3

    = (4/3)××33

    = 4××9

    = 36 cm3

    Length of the wire, h = 36 m = 3600 cm

    Since the sphere is melted and drawn into a wire, volume remains the same.

    Volume of the wire, r2h = 36

    r2×3600 = 36

    r2 = 1/100

    r = 1/10 = 0.1 cm = 1 mm

    Hence the radius of the wire is 1 mm.

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