Question : Some medicine in liquid form is prepared in a hemispherical container of diameter 36 cm. When the container is full of medicine, the medicine is transferred to small cylindrical bottles of diameter 6 cm and height 6 cm. How many bottles are required to empty the container?
Option 1: 76
Option 2: 72
Option 3: 70
Option 4: 75
Correct Answer: 72
Solution :
Diameter of hemisphere = 36 cm
Radius, $R$ = 18 cm
Diameter of cylinder = 6 cm
Radius, $r$ = 3 cm
Height of cylinder = 6 cm
Let $n$ be the number of cylinders,
Volume of hemisphere = Volume of all cylinders
$\frac{2}{3} \pi R^3 = n × \pi r^2 h$
⇒ $\frac{2}{3} ×\pi ×18^3 = n × \pi × 3^2 ×6$
⇒ $n = \frac{2 × 18 × 18 × 18}{9 × 6 × 3}$
⇒ $n = 72$
Hence, the correct answer is 72.
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