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Question
A right circular cylinder having diameter 12 cm and height 15 cm is full ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.
Solution
We have
Radius of the cylincler = `12/2` = 6 cm
Height of the cylinder = 15 cm
∴ Volume of the cy linder = πr2h
= π × 62 × 15
= 540π cm3
Radius of the ice-cream cone = 3 cm
Height of the ice-cream cone = 12 cm
∴ Volume of the conical part of ice-cream cone = `1/3 pir^2h`
Volume of the conical part of ice-cream cone = `1/3 xx pi xx 3^2 xx 12 cm^3`
Volume of the conical part of ice-cream cone = 36π cm3
Volume of the hemispherical top of the ice-cream = `2/3pir^3`
= `2/3 xx pi xx 3^3`
= 18π cm3
Total volume of the ice-cream cone
= (36π + 18π) cm3
= 54π cm3
∴ Number of ice-cream cone
= `"Volume of the cylinder"/"Total volume of ice-cream"`
= `(540pi)/(54pi)`
= 10
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