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Deepak Bora
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A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter 4[2/3] cm and height 3 cm. Find the number of cones so formed.

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In the given problem given shape is sphere.  To find answer of this question need to use sphere volume formula. Given problem from RS Aggarwal book page number 829, problem number 39, chapter volume and surface area of solid, exercise 17D,Chapter Mensuration

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  1. Diameter of metallic sphere D=28 cm

    Diameter of circular base of smaller cone d=432 cm=314 cm

    Hight of cone h=3 cm

    Hence,

    Radius of metallic sphere R=2D=14 cm

    Radius of circular base of smaller cone r=2d=37 cm

    Volume of metallic sphere V=34πR^3

                                                     =34×722×(14)3 cm3

                                                     =34×722×(14)3 cm^3

                                                     =2188×2744 cm^3

                                                     =88×130.667 cm^3
    .
     Volume of metallic sphere V=11498.667 cm^3

    Volume of one cone v=31π r^2 h

                                      =31×722×(37)2×3 cm^3

                                       =2166×(949) cm^3

    Volume of one cone=17.111 cm^3

    Number of cones formed n=Volume of one cone (v)Volume of sphere(V)

    n=11498.667 cm^3​ /17.111 cm^3
    n=672

    Hence the solid sphere can be melted in 672 smaller cones .

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