A hemispherical bowl of internal diameter 30 cm is full of a liquid.

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?

Solution:

Radius of hemispherical ball $=\frac{30}{2}=15 \mathrm{~cm}$

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

$=\left(\frac{2}{3} \pi \times 15 \times 15 \times 15\right) \mathrm{cm}^{3}$

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

Height of each bottle $=6 \mathrm{~cm}$

Volume of each bottle $=\pi r^{2} h$

$=\left(\pi \times \frac{5}{2} \times \frac{5}{2} \times 6\right) \mathrm{cm}^{3}$

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

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

$=60$

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