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Deepak Bora
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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. 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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