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Deepak Bora
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A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. Find the number of cones thus obtained.

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An Important Question of class 10 Based on Mensuration Chapter of M.L Aggarwal for ICSE BOARD.
A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius and height are given.Then you have to find the number of cones thus obtained.
This is the Question Number 23, Exercise 17.5 of M.L Aggarwal.

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  1. Given radius of the metallic sphere, R = 10.5 cm

    Volume of the sphere = (4/3)R3

    = (4/3)×10.53

    = 1543.5 cm3

    Radius of cone, r = 3.5 cm

    Height of the cone, h = 3 cm

    Volume of the cone = (1/3)r2h

    = (1/3)×3.52×3

    = 12.25 cm3

    Number of cones made from sphere = Volume of sphere / volume of cone

    = 1543.5 /12.25

    = 126

    Hence the number of cones that can be made is 126.

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