Question

A hemispherical bowl of internal radius 9 cm is full of water. This water is to be filled in cylindrical bottles of diameter 3 cm and height 4 cm. Find the number of bottles needed in which the water can be filled.

Answer 1

Radius of hemisphere = 9 cm
Volume of hemisphere$=\frac{2}{3}\mathrm{\pi }{\mathrm{r}}^3$
$=\left(\frac{2}{3}\mathrm{\pi }\times 9\times 9\times 9\right){\text{cm}}^3$
Radius of each bottle = $\frac{3}{2}\mathrm{cm}$
Height of each bottle = 4 cm
Volume of each bottle$=\mathrm{\pi }{r}^{2}h$
$=\left(\mathrm{\pi }\times \frac{3}{2}\times \frac{3}{2}\times 4\right){\text{cm}}^3$

Number of bottles$=\frac{\text{Volume of the hemisphere}}{\text{Volume of each bottle}}$
$$\begin{gathered} =\frac{2\mathrm{\pi }\times 9\times 9\times 9\times 2\times 2}{3\times \mathrm{\pi }\times 3\times 3\times 4} \\ =54 \end{gathered}$$