Question

A cubical ice-cream brick of edge 22 cm is to be distributed among some children by filling ice-cream cones of radius 2 cm and height 7 cm up to the brim. How many children will get the ice-cream cones?
(a) 163
(b) 263
(c) 363
(d) 463

Answer 1

(c) 363
The edge of the cubical ice-cream brick = a = 22 cm
Volume of the cubical ice-cream brick$={\left(a\right)}^3$
$=\left(22\times 22\times 22\right){\text{cm}}^3$

Radius of an ice-cream cone = 2 cm
Height of an ice-cream cone = 7 cm
Volume of each ice-cream cone$=\frac{1}{3}\mathrm{\pi }{r}^{2}h$
$=\left(\frac{1}{3}\times \frac{22}{7}\times 2\times 2\times 7\right){\text{cm}}^3$

Number of ice-cream cones$=\frac{\text{Volume of the cubical ice cream brick}}{\text{Volume of each ice cream cone}}$

$$\begin{gathered} =\frac{22\times 22\times 22\times 3\times 7}{22\times 2\times 2\times 7} \\ =363 \end{gathered}$$
Hence, the number of ice-cream cones is 363.