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.

Answer 1

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