Question : A hemispherical bowl of internal diameter 18 cm contains water. This water is to be filled in cylindrical bottles of diameter 6 cm and height 3 cm. The number of bottles required to empty the bowl is:
Option 1: 3
Option 2: 9
Option 3: 6
Option 4: 18
Correct Answer: 18
Solution :
The volume of a hemisphere is $\frac{2}{3}\pi r^3$.
Given that the diameter of the hemisphere is 18 cm, the radius$(r)$ is 9 cm.
$\therefore$ The volume of the hemisphere = $\frac{2}{3}\pi (9)^3 = 486 \pi \text{ cm}^3$
The volume of a cylinder is $\pi r^2h$.
Given that the diameter of the cylinder is 6 cm, the radius$(r)$ is 3 cm, and the height$(h)$ is 3 cm.
$\therefore$ The volume of the cylinder = $\pi (3)^2(3) = 27 \pi \text{ cm}^3$
The number of bottles required to empty the bowl = $\frac{486 \pi \text{ cm}^3}{27 \pi \text{ cm}^3}$ = 18
Hence, the correct answer is 18.
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