Question

A cubical ice cream brick of edge length 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

Hint: In order to find the number of ice cream cones, we calculate the volume of the ice cream brick and the volume of each ice cream cone. We divide both the volumes to find the number of cones.

Complete Step-by-Step solution:
Given Data,
Ice cream brick of edge length 22cm.
Now we know the volume of a cube of side ‘a’ is given by ${{\text{a}}^3}$.
Volume of ice cream brick = ${22^3}$= 10648 cm$^3$.

Let the number of ice cream cones children get be a variable ‘x’.
The volume of the ice cream brick is transferred into some x number of ice cream cones. Total volume of the ice cream remains constant.
The shape of an ice cream cone is a hollow conical shape, the volume of a cone of height h, radius r is given by $\dfrac{1}{3}\pi {{\text{r}}^2}{\text{h}}$.
Hence, volume constant
$ \Rightarrow {{\text{a}}^3} = {\text{x }} \times {\text{ }}\dfrac{1}{3}\pi {{\text{r}}^2}{\text{h}}$
Given r = 2cm and h = 7cm.
$
   \Rightarrow 10648 = {\text{x }} \times {\text{ }}\dfrac{1}{3}.\pi {.2^2}.7 \\
   \Rightarrow {\text{x = }}\dfrac{{{\text{3 }} \times {\text{ 10648}}}}{{3.14 \times 4 \times 7}} \\
   \Rightarrow {\text{x = 363}} \\
$
Hence the ice cream brick is filled into 363 cones.

Note: In order to solve this type of question the key is to understand that the volume of the total ice cream has not changed, it was only converted from one form to another. Upon knowing this we apply the formulae of volumes of a cube and a cone and form a relation. Solving this gave us the number of cones.