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.

Answer 1

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