Question

A cubical ice-cream brick of edge $22cm$ is to be distributed among some children by filling ice cream cones of radius $2cm$ and height $7cm$ up its brim, how many children will get ice cream cones?

Answer 1

Given: Edge of cubical ice-cream brick, $a=22cm$

The radius of the ice cream cones, $r=2cm$

Height of the ice cream, $h=7cm$

Let the number of ice cream cones be $x$.

It is given that the small ice cream cones will be filled with a cubical ice-cream brick.

$\therefore$ Number of small ice cream cones $\times$ Volume of a small ice cream cone $=$ Volume of the cubical ice cream brick

$\Rightarrow x\times \frac{1}{3}\pi r^{2}h=a^3$ [$\because$ Volume of cone $=\frac{1}{3}\pi r^{2}h,$ Volume of cube $=(Edge{)}^3$]

$\Rightarrow x\times \frac{1}{3}\times \frac{22}{7}\times 2\times 2\times 7={22}^3$

$\Rightarrow x=\frac{22\times 22\times 3}{4}$

$\Rightarrow x=121\times 3$

$\Rightarrow x=363$ cones

Hence, $363$ children will get small ice cream cones.