Question

A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be filled into cylindrical-shaped bottles each of diameter 5 cm and height 6 cm. Find the number of bottles necessary to empty the bowl.

Answer 1

Inner diameter of the bowl = 30 cm

Inner radius of the bowl = 15 cm

Volume of liquid in it $=\frac{2}{3}\pi \times r^3=\frac{2}{3}\pi \times {15}^{3}c{m}^3$

Radius of each cylinder bottle = 2.5 cm and its height = 6 cm.

Volume of each cylindrical bottle $=\pi r^{2}h=\pi \times (\frac{5}{2}{)}^2\times 6c{m}^2=\frac{25}{4}\times 6\pi =\frac{75\pi }{2}c{m}^3$

$\text{Required number of bottles}=\frac{\text{Volume of liquid}}{\text{Volume of each cylindrical bottle}}=\frac{\frac{2}{3}\times \pi \times 15\times 15\times 15}{\frac{75}{2}\times \pi }=60$

Hence, bottles required = 60