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?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 2 i.e. 36
Given that
The radius of a hemispherical bowl (R) = 6 cm
The radius of a cylindrical bottle (r) = Diameter/2 = 2/2 = 1 cm
The height of a cylindrical bottle (h) = 4 cm
Formula used
The volume of a hemisphere = (2/3)πR3 cubic units
The volume of a cylinder = πr2h cubic units
Let the number of cylindrical bottle be N
Calculation
Volume of a hemispherical bowl = N × Volume of a cylinderical bottle
⇒ (2/3)πR3 = N × πr2h
⇒ (2/3) × 63 = N × 12 × 4 = 4N
⇒ N = 36