A hemispherical bowl of internal diameter 18 cm contains water. This water is to be filled in cylindrical bottles of diameter 6cm and height 3 cm. The number of bottles required to empty the bowl is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 18.
A hemispherical bowl of internal diameter 18 cm
Cylindrical bottles of diameter 6 cm and height 3 cm
Volume of Hemisphere =2πr3/3
Volume of Cylinder = πr2h
Radius of hemispherical bowl = 18/2 = 9
Volume of water in hemispherical bowl = 2πr3/3 = (2 × 22 × 9 × 9 × 9)/(3 × 7)
Radius of cylindrical bottle = 6/2 = 3
Volume of 1 cylindrical bottle = πr2h = (22 × 3 × 3 × 3)/7
Let the number of required bottles = x
ATQ -
Volume of hemispherical bowl = Volume of 1 cylindrical bowl × Number of required bottles
(2 × 22 × 9 × 9 × 9)/(3 × 7) = (22 × 3 × 3 × 3)x/7
(2 × 9 × 9 × 9)/3 = (3 × 3 × 3)x
x = 18