# A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and the height of the cone is 4 cm. The solid is placed in a cylindrical tub full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and its height is 9.8 cm, find the volume of the water left in the tub.

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This question from
RS Aggarwal
Chapter Mensuration
Volume and surface
Volume and Surface Area of Solid
Exercise 17A
Page number 788
Problem number 21

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### 1 Answer

1. Radius of hemisphere = 2.1 cm

Volume of hemisphere = [2/3] πr³

= [2/3] × [22/7] × [2. 1]³

Volume of hemisphere  = 19. 404 cm³

Height of cone = 4 cm

Volume of cone = [1/3] πr²h

= [1/3] × [22/7] × [2. 1]² ×4

= 18. 48 cm³

Volume of the object = 18. 48 +19. 404

= 37. 884 cm³

Volume of cylindrical tub = πr²h

= [22/7] × 5² ×9. 8

= 770 cm³

When the object is immersed in the tub, volume of water equal to the volume of the object is displaced from the tub.

Volume of water left in the tub = 770 -37. 884

= 732. 116 cm³

∴ Volume of the water left in the tub is 732. 116 cm³

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