Question

A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm. How many bottles are required to empty the bowl?

Answer 1

Internal radius of the hemispherical bowl = 9 cm
Radius of a cylindrical shaped bottle = 1.5 cm
Height of a bottle = 4 cm

Number of bottles required to empty the bowl = $\frac{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{hemispherical}\mathrm{bowl}}{\mathrm{volume}\mathrm{of}\mathrm{a}\mathrm{cylindrical}\mathrm{shaped}\mathrm{bottle}}$
$$\begin{gathered} =\frac{{\displaystyle \frac{2}{3}}\mathrm{\pi }\times 9^3}{\mathrm{\pi }\times 1.5^2\times 4} \\ =\frac{2\times 9\times 9\times 9}{3\times 1.5\times 1.5\times 4} \\ =54 \end{gathered}$$

∴ 54 bottles are required to empty the bowl.