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

âˆ´radius of the cylindrical part = 3.5 cm

Volume of hemisphere = [2/3] Ï€rÂ³

= [2/3] Ã— [22/7] Ã— 3. 5Â³

= 89. 83 cmÂ³

Volume of the cylinder = Ï€rÂ²h

= [22/7] Ã— [3. 5]Â² Ã—6. 5

= 250. 25 cmÂ³

Height of cone = 12. 8 -6. 5

Height of cone = 6. 3 cm

Volume of the cone = [1/3] Ï€rÂ²h

= [1/3] [22/7] [3.5]Â² Ã— 6. 3

= 80. 85 cmÂ³

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

= 420. 93 cmÂ³

âˆ´ Volume of the solid is 420. 93 cmÂ³