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?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 72.
Given that
A hemispherical container of diameter 36 cm
Radius (R) = 36/2 = 18 cm
Let there be N small cylindrical bottles of diameter 6 cm and height 6 cm
radius of cylindrical bottles r = 6/2 = 3 cm
Volume of a hemisphere = (2/3)πR3 cubic units
The volume of a cylinder = π r² h cubic units
Volume of a hemispherical container = N × Volume of small cylindrical bottles
(2/3)πR3 = N × π r² h
⇒ (2/3) × 183 = N × 32 × 6
⇒ N = 72