A hemispherical bowl of internal radius 9 cm is full of water. This water is to be filled in cylindrical bottles of diameter 3 cm and height 4 cm. find the number of bottles needed to fill the whole water of the bowl.
Given: Radius of hemisphere = rh = 9 cm
Diameter of cylindrical shaped bottles = 3 cm
∴ radius of cylindrical shaped bottles = rc = 3/2 = 1.5 cm
Height of cylindrical shaped bottle = h = 4 cm
Formula: volume of hemisphere = (volume of sphere/2) = (2/3)πrh3
Volume of cylinder = πrc2h
Let ‘n’ bottles are required
As we are filling the cylindrical bottles with liquid in hemispherical bowl hence we can say that
volume of liquid in cylindrical bottles = volume of liquid in hemisphere
∴ n × π × rc2 × h = (2/3) × π × rh3
n × (3/2)2 × 4 × 3 = 2 × 93
n = 33 × 2
n = 27 × 2
n = 54
Therefore 54 cylindrical shaped bottles are required to fill the liquid from hemispherical bowl.