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Question
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.
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Solution
External radius of a hollow sphere, R = 8 cm
And, internal radius, r = 6 cm
∴ Volume of hollow sphere = `4/3 pi(R^3 - r^3)`
`= 4/3 pi(8^3 - 6^3)`
`= 4/3 pi(512 - 216)`
`= (4/3 pi xx 296) cm^3`
Radius of cone = 2 cm, height = 8 cm
∴ Volume of cone = `1/3 pi(2)^2 xx 8 = (32/3 pi) cm^3`
Thus number of cones formed = `"Volume of hollow sphere"/"volume of cone"`
`= (4/3 pi xx 296)/(32/3 pi)`
= 37
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