The given figure represent a solid consisting of a cylinder surmounted by a cone at one end a hemisphere at the other. Find the volume of the solid.

The solid consisting of a cylinder surmounted by a cone at one end a hemisphere at the other.


Length of cylinder = l = 6.5 cm


Diameter of cylinder = 7 cm


Radius of cylinder = r = Diameter ÷ 2 = 7/2 cm = 3.5 cm


Volume of cylinder = πr2l


= 22/7 × 3.5 × 3.5 × 6.5 cm3


= 250.25 cm3


Length of cone = l’ = 12.8 cm – 6.5 cm = 6.3 cm


Diameter of cone = 7 cm


Radius of cone = r = Diameter ÷ 2 = 7/2 cm = 3.5 cm


Volume of cone = 1/3 πr2l’


= 1/3 × 22/7 × 3.5 × 3.5 × 6.3 cm3


= 80.85 cm3


Diameter of hemisphere = 7 cm


Radius of hemisphere = r = Diameter ÷ 2 = 7/2 cm = 3.5 cm


Volume of hemisphere = 2/3 πr3


= 2/3 × 22/7 × 3.5 × 3.5 × 3.5 cm3


= 89.83 cm3


Volume of the solid = Volume of cylinder + Volume of cone + Volume of hemisphere


Volume of solid = 250.25 cm3 + 80.85 cm3 + 89.83 cm3


= 420.93 cm3


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