A right circular cylinder having diameter 12 cm and height 15 cm is full of 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.

Explanation

For cylinder,
diameter = 12 cm
`:.` its radius (r ) == 6 cm
its height (h) = 15 cm.
for conical part of ice cream,
diameter = 6 cm
its radius `(r_(1)) = 3 cm`
height `(h_(1)) = 12 cm`
For hemispherical part of ice cream
radius = `(r_(1)) = 3 cm`
volume of cylinder `= pi r^(2) h` ltbgt `= pi xx ^(2) xx 15 cm^(3)`
`540 pi cm^(3)`
Volume of conical part of ice cream `= (1)/(3) pi r_(1)^(2) h_(1)`
`= (1)/(3) pi xx 3^(2) xx 12`
`36 pi cm^(3)`
volume of hemispherical part of the cone `= (2)/(3) pi r_(1)^(3)`
`= (2)/(3) xx pi xx 3^(3)`
`= 18 pi cm^(3)`
Total volume of ice-cream `= 36 pi + 18 pi = 54 cm^(2)`
Number of ice-cream cones `= ("Volume of the cylinder")/("Total volume of ice-cream cone")`
`= (540 pi)/(54 pi)`
= 10