Question : A hemispherical bowl of internal radius 6 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 2 cm and height 4 cm. How many bottles will be needed to empty the bowl?
Option 1: 32
Option 2: 37
Option 3: 38
Option 4: 36
Correct Answer: 36
Solution :
The volume of a hemisphere = $\frac{2}{3}\pi r^3$, where $r$ = radius
Given that the radius of the hemisphere is 6 cm.
The volume of the hemisphere = $\frac{2}{3}\pi (6)^3 = 144\pi \, \text{cm}^3$
The volume of a cylinder = $\pi r^2h$
Given that the diameter of the cylinder is 2 cm.
So, the radius is 1 cm, and the height is 4 cm.
The volume of the cylinder = $\pi (1)^2(4) = 4\pi \, \text{cm}^3$
$\therefore$ The required number of bottles is needed to empty the bowl = $\frac{144\pi}{4\pi}$ = 36
Hence, the correct answer is 36.
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