Q. 274.0( 25 Votes )

# 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.

Answer :

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 = πr^{2}l

= 22/7 × 3.5 × 3.5 × 6.5 cm^{3}

= 250.25 cm^{3}

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 πr^{2}l’

= 1/3 × 22/7 × 3.5 × 3.5 × 6.3 cm^{3}

= 80.85 cm^{3}

Diameter of hemisphere = 7 cm

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

Volume of hemisphere = 2/3 πr^{3}

= 2/3 × 22/7 × 3.5 × 3.5 × 3.5 cm^{3}

= 89.83 cm^{3}

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

Volume of solid = 250.25 cm^{3} + 80.85 cm^{3} + 89.83 cm^{3}

= 420.93 cm^{3}

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