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