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A metallic sphere of radius 10.5 cm is melted and then recast into smaller cones , each of radius 3.5 cm and height 3 cm. How many cones are obtained?

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Given

Radius of metallic sphere R = 10.5 cm

Radius of circular base of smaller cone r = 3.5 cm

Height of cone h = 3 cm

Volume of metallic sphere

Volume of metallic sphere V = 4851 cm3

Volume of one cone v = 1/3 πr2h

Volume of one cone = 38.5 cm3

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

n = 4851 cm3/38.5 cm3

n = 126

Hence the solid sphere can be melted in 126 smaller cones.

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