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Question
A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into toys with the shape of a right circular cone mounted on a hemisphere of radius 3 cm.If the height of the toy is 12 cm, find the number of toys so formed.
Solution
Diameter of cylinder = 12 cm
Therefore
r = 6 cm
Height = 15 cm
Therefore,
Volume of cylinder
`=pir^2 h`
`=36 xx 15 xx pi cm^3`
Therefore,
Volume of toy = volume of cone + volume of hemisphere
`=1/3pir^2h + 2/3 pir^3`
`=1/3pir^2(h+2r)`
`=1/3 pi xx 3 xx 3(9 + 2 xx 3)`
` = 45 pi cm^3`
Therefore,
No. of toys
` ="volume of cylinder"/"volume of toy"`
`=(36 xx 15 xx pi)/(45 xx pi)`
`=12`
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