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.
Deepak BoraNewbie
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