A hemisphere bowl of internal diameter 30 cm is full of a liquid. This liquid is filled into cylindrical - shapes bottles each of diameter 5 cm and height 6 cm. How many bottles are required?
Given: diameter of hemisphere = 30 cm
∴ Radius of hemisphere = rh = 30/2 = 15cm
Diameter of cylindrical shaped bottles = 5 cm
∴ radius of cylindrical shaped bottles = 5/2 = rc = 2.5 cm
Height of cylindrical shaped bottle = h = 6 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 × 2.52 × 6 × 3 = 2 × 153
n × 6.25 × 9 = 3375
n = 3375/56.25
n = 60
Therefore 60 cylindrical shaped bottles are required to fill the liquid from hemispherical bowl.