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Question
A solid metallic hemisphere of diameter 28 cm is melted and recast into a number of identical solid cones, each of diameter 14 cm and height 8 cm. Find the number of cones so formed.
Solution
Given - diameter 14 cm; height 8 cm; n = number of cones
Volume of hemisphere = n × Volume of 1 cone
∴ `2/3 piR^3 = n xx 1/3 pir^2h`
∴ `2/cancel(3) cancel(pi)R^3 = n xx 1/cancel(3) cancel(pi)r^2h`
∴ 2(14)3 = n(7)2(8)
∴ `(2 xx 14 xx 14 xx 14)/(7 xx 7 xx 8) = n`
∴ n = 14
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