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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
Let the number of small cones be 'n'
Volume of sphere
= `4/3pi(8^3 - 6^3)`
= `4/3 xx pi xx 2 xx 148`
Volume of small cones
= `1/3pir^2h`
= `1/3 xx pi xx 2^2 xx 4`
Volume of sphere = n × Volume of small cones
`=> 4/3 xx pi xx 2 xx 148 = n xx 1/3 xx pi xx 2^2 xx 8`
`=> n = (4 xx 2 xx 148 xx 3)/(4 xx 8 xx 3)`
`=>` n = 37
The number of cones = 37 cm.
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