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.

Answer 1

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`