A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 3.5 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 cylindrical tub is 5 cm and its height is 10.5 cm, find the volume of water left in the cylindrical tub (use π = 22/7) = (Ans: 683.83 cm³)

Ans:    No. of solid = vol of cone + vol of hemisphere

= 1/3 π r² h + 2/3 π r³

= 1/3 π r² [h +2 r]

On substituting we get,

= 141.17 cm³

vol of cylinder = π r² h

On substituting we get,

= 825 cm³

volume of H₂O left in the cylinder = 825 - 141.17

= 683.83 cm³