A cylindrical ice-cream container, completely filled with ice-cream has 22 cm radius and 24 cm height. If this ice-cream is to be distributed among some children by filling it in the cone of radius 2 cm, height 7 cm and upper part of the cone which is hemisphere, then how many children will get the ice-cream cones?

In ice-cream cylinder,

Radius of cylinder (R) = 22 cm

Height (H) = 24 cm

In each ice-cream cone,

Radius of cone part = Radius of hemisphere part = (r) = 2 cm

Height (h) = 7 cm

Let the number of children who get ice cream cone be n.

Volume of ice-cream cylinder = n × Volume of ice-cream cone

$\Rightarrow πR^2H = n \times \Big(\dfrac{1}{3}πr^2h + \dfrac{2}{3}πr^3\Big) \\[1em] \Rightarrow πR^2H = n \times π \times \Big(\dfrac{r^2h + 2r^3}{3}\Big) \\[1em] \Rightarrow R^2H = n \times \Big(\dfrac{r^2h + 2r^3}{3}\Big) \\[1em] \Rightarrow 22^2 \times 24 = n \times \Big(\dfrac{2^2 \times 7 + 2 \times 2^3}{3}\Big)\\[1em] \Rightarrow 11616 = n \times \dfrac{28 + 16}{3} \\[1em] \Rightarrow n = \dfrac{11616 \times 3}{44} \\[1em] \Rightarrow n = \dfrac{34848}{44} = 792.$

Hence, number of children who get ice cream cone = 792.