This is important problem for complex structure to solve it easily. This problem from RS Aggarwal book chapter Volume and Surface area of solid page number 288 exercise 17A.

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# The adjoining figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other. Find the volume of the solid.

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Given data,

Diameter of the cylindrical part =7 cm

∴radius of the cylindrical part = 3.5 cm

Volume of hemisphere = [2/3] πr³

= [2/3] × [22/7] × 3. 5³

= 89. 83 cm³

Volume of the cylinder = πr²h

= [22/7] × [3. 5]² ×6. 5

= 250. 25 cm³

Height of cone = 12. 8 -6. 5

Height of cone = 6. 3 cm

Volume of the cone = [1/3] πr²h

= [1/3] [22/7] [3.5]² × 6. 3

= 80. 85 cm³

Total volume = 89. 83 +250. 25 +80. 85

= 420. 93 cm³

∴ Volume of the solid is 420. 93 cm³