Question

A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be poured into cylindrical bottles of diameter 5 cm and height 6 cm each. Find the number of bottles required.

Answer 1

Inner diameter of the bowl = 30 cm
Inner radius of the bowl$=\frac{30cm}{2}=15cm$
Inner volume of the bowl = Volume of liquid $=\frac{2}{3}{\mathrm{\pi r}}^3=\frac{2}{3}\times \mathrm{\pi }\times {15}^3{\mathrm{cm}}^3$

Radius of each bottle = 2.5 cm
Height = 6 cm

Volume of each bottle$={\mathrm{\pi r}}^2\mathrm{h}=\mathrm{\pi }\times \frac{5}{2}\times \frac{5}{2}\times 6=\frac{75\mathrm{\pi }}{2}{\mathrm{cm}}^3$

Total number of bottles required $=\frac{\left[{\displaystyle \frac{2}{3}}\mathrm{\pi }\times 15\times 15\times 15\right]}{{\displaystyle \frac{75\mathrm{\pi }}{2}}}=\frac{2\mathrm{\pi }\times 15\times 15\times 15\times 2}{3\times 75\mathrm{\pi }}=15\times 4=60$