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RS Aggarwal

Chapter Mensuration

Volume and surface

Volume and Surface Area of Solid

Exercise 17A

Page number 787

Problem number 17

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# A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder. The diameter of the hemisphere is 21 cm and the total height of the vessel is 14.5 cm. Find its capacity

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This answer was edited.Diameter of the hemisphere = 21 cm

∴ radius of the hemisphere = 10.5 cm

Volume of the hemisphere = [2/3] × πr³

= [2/3] × 3.14 ×10. 5 ×10. 5 ×10. 5

= 2425. 5 cm³

Height of the cylinder = Total height of the vessel-Radius of the hemisphere = 14. 5 -10. 5 = 4 cm

Volume of the cylinder = πr²h

= [22/7] × 10. 5 × 10. 5 ×4

= 1386 cm³

Total volume = Volume of hemispherical part +Volume of cylinder

= 1386 +2425. 5

= 3811. 5 cm³

∴ Capacity of the vessel is 3811. 5 cm³