A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into
72 cylindrical bottles of diameter 6 cm. Find the height of the each bottle, if 10% liquid
is wasted in this transfer
Answers
Diameter of hemispherical bowl = 36 cm
Radius of hemispherical bowl = 18 cm
Volume of hemispherical bowl = (2/3 × 22/ 7 x r^3
=( 2/3 × 22/7 x 18 x 18 x 18)cm^3
Volume of liquid wasted = 10%
Therefore, Remaining Volume = 90% x Volume of hemispherical bowl
Number of cylinders = 72
Diameter of each cylinder = 6 cm
Radius of each cylinder = 3 cm
Height of the cylinder = ?
Let the Height of the Cylinder be h
Volume of cylinder = 22/7 x r^2 × h
= (22/7 x 3 x 3 x h) cm^3
Volume of 72 cylinders = 72 x (22/7 × 3 x 3 x h ) cm^3
90% x Volume of hemispherical bowl = Volume of 72 cylinders
90/100 × 2/3 x 22/7 x 18 x 18 x 18 = 72 x 22/7 x 3 x 3 x h
= 9/10 × 2 x 18 x 18 x 18 = 72 x 3 x 3 x 3 x h
= 1/10 x 2 x 6 x 6 x 6 = 8 x h
= 6 x 6 x 6 = 40h
= 3 x 3 x 3 = 5h
= 27/5 = h
h = 5.4 cm