This is the Important question of class 10 Based on Mensuration Chapter of M.L Aggarwal book for ICSE BOARD.
In this question certain number of metallic cones each of radius and height is given are melted and recast in a solid sphere of radius 6 cm.So, Find the number of cones.
This is the Question Number 24, Exercise 17.5 of M.L Aggarwal.
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A certain number of metallic cones each of radius 2 cm and height 3 cm are melted and recast in a solid sphere of radius 6 cm. Find the number of cones.
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Given radius of metallic cones, r = 2 cm
Height of cone, h = 3 cm
Volume of cone = (1/3)r2h
= (1/3)×22×3
= 4 cm3
Radius of the solid sphere, R = 6 cm
Volume of the solid sphere = (4/3)R3
= (4/3)63
= 4××2×6×6
= 288 cm3
Number of cones made from sphere = Volume of solid sphere / volume of the cone
= 288/4
= 72
Hence the number of cones that can be made is 72.