• 1
Newbie

# 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.

• 1

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

Share

1. Radius of hemisphere = 2.1 cm

Volume of hemisphere = [2/3] Ï€rÂ³

= [2/3] Ã— [22/7] Ã— [2. 1]Â³

Volume of hemisphere Â = 19. 404 cmÂ³

Height of cone = 4 cm

Volume of cone = [1/3] Ï€rÂ²h

= [1/3] Ã— [22/7] Ã— [2. 1]Â² Ã—4

= 18. 48 cmÂ³

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

= 37. 884 cmÂ³

Volume of cylindrical tub = Ï€rÂ²h

= [22/7] Ã— 5Â² Ã—9. 8

= 770 cmÂ³

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 cmÂ³

âˆ´ Volume of the water left in the tub is 732. 116 cmÂ³

• 0