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Deepak Bora
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The surface area of a solid metallic sphere is 616 cm square. It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained?

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This question is Based on Mensuration Chapter of M.L Aggarwal book for ICSE BOARD for class 10.
The surface area of a solid metallic sphere is given. It is melted and recast into smaller spheres of given diameter. You have to find How many such spheres can be obtained?
This is the Question Number 26, Exercise 17.5 of M.L Aggarwal.

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  1. Given surface area of the sphere = 616 cm2

    4R2 = 616

    4×(22/7)R2 = 616

    R2 = 616×7/4×22

    R2 = 49

    R = 7

    Volume of the solid metallic sphere = (4/3)R3

    = (4/3)×73

    = (1372/3) cm3

    Diameter of smaller sphere = 3.5 cm

    So radius, r = 3.5/2 = 7/4 cm

    Volume of the smaller sphere = (4/3)r3

    = (4/3)×(7/4)3

    = (343/48) cm3

    Number of spheres made = Volume of the solid metallic sphere/ Volume of the smaller sphere

    = (1372/3) ÷(343/48)

    =1372×48/(3×343)

    = 64

    Hence the number of spheres made is 64.

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