Question : A hemispherical bowl of internal radius 18 cm is full of liquid. This liquid is to be filled in cylindrical bottles each of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl?
Option 1: 72
Option 2: 70
Option 3: 68
Option 4: 66
Correct Answer: 72
Solution :
Given:
Internal radius of hemispherical bowl = 18 cm
Internal radius of bottle = 3 cm
The internal height of the bottle = 6 cm
Total volume of liquid in hemisphere = $\frac{2}{3} × π ×18^3= 3888π$ cm
3
Let the number of bottles be $n$.
According to the question:
$3888π = n × π × (3)^2 × 6$
⇒ $n=\frac{3888}{9\times6}$
⇒ $n = 72$
Hence, the correct answer is 72.
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