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${\displaystyle =\frac{30}{2}=15 \text{cm}}$

Volume of hemispherical bowl${\displaystyle =\frac{2}{3}\pi {\text{r}}^3}$

${\displaystyle =(\frac{2}{3}\pi \times 15\times 15\times 15){\text{cm}}^3}$

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

Height of each bottle = 6 cm

Volume of each bottle =πr²h

${\displaystyle =(\pi \times \frac{5}{2}\times \frac{5}{2}\times 6){\text{cm}}^3}$

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

${\displaystyle =\frac{2\times \pi \times 15\times 15\times 2\times 2}{3\times \pi \times 5\times 5\times 6}}$

=60