#### 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 = 6cm

Height of the cylinder = 15cm

∴ volume of the cylinder = πr^{2}h

= π x 6^{2} x 15

= 540πcm^{3}

Radius of the ice-cream cone = 3cm

Height of the ice-cream cone = 12cm

∴ valume of the conical part of ice-cream

cone = `1/3 pir^2h`

valume of the conical part of ice-cream

cone = `1/3xxpixx3^2xx12cm^3`

valume of the conical part of ice-cream

cone = 36πcm^{3}

volume of the hemispherical top of the ice-cream =`2/3pir^3=2/3xxpixx3^3`]

= 18πcm^{3}

Total volume of the ice-cream

cone = (36π+18π)cm^{3} = 54πcm^{3}

∴ Number of ice-cream cone= `"volume of the cylinder"/"Total volume of ice-cream"`

=`(540pi)/(54pi)` = 10