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The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed.

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Rd sharma class 10 maths exercise-16.1 mensuration.

In this question we have to find the diameter of the base of the cone having                                                                the surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a cone of height 28 cm.

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  1. Given,

    The height of the cone = 28 cm

    Surface area of the solid metallic sphere = 616 cm3

    We know that,

    Surface area of the sphere = 4πr2

    So, 4πr2 = 616

    r2 = 49

    r = 7

    Radius of the solid metallic sphere = 7 cm

    Let’s assume r to be the radius of the cone

    We know that,

    Volume of the cone = 1/3 πr2h

    = 1/3 πr2 (28) ….. (i)

    Volume of the sphere = 4/3 πr3

    = 4/3 π73 ………. (ii)

    On equating equations (i) and (ii), we have

    1/3 πr2 (28) = 4/3 π73

    Eliminating the common terms, we get

    r2 (28) = 4 x 73

    r2 = 49

    r =7

    So, diameter of the cone = 7 x 2 = 14 cm

    Therefore, the diameter of the base of the cone is 14 cm

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