Question

A hemispherical bowl of internal diameter 30 cm is full of a liquid. This liquid is poured into cylindrical bottles of diameter 5 cm and height 6 cm each. How many bottles are required?

Answer 1

Radius of hemispherical ball = $\frac{30}{2}=15\mathrm{cm}$
Volume of hemispherical bowl$=\frac{2}{3}\mathrm{\pi }{\mathrm{r}}^3$
$=\left(\frac{2}{3}\mathrm{\pi }\times 15\times 15\times 15\right){\text{cm}}^3$

Radius of each bottle = $\frac{5}{2}\mathrm{cm}$

Height of each bottle = 6 cm

Volume of each bottle$=\mathrm{\pi }{r}^{2}h$
$=\left(\mathrm{\pi }\times \frac{5}{2}\times \frac{5}{2}\times 6\right){\text{cm}}^3$

Number of bottles required$=\frac{\text{Volume of the hemispherical bowl}}{\text{Volume of each bottle}}$

$$\begin{gathered} =\frac{2\times \mathrm{\pi }\times 15\times 15\times 15\times 2\times 2}{3\times \mathrm{\pi }\times 5\times 5\times 6} \\ =60 \end{gathered}$$