A conical vessel of radius 6 cm and height 8 cm is filled with water. A sphere is lowered into the water and its size is such that when it touches the sides of the conical vessel, it is just immersed. How much water will remain in the cone after the overflow?

A conical vessel of radius 6 cm and height 8 cm is filled with

water. A sphere is lowered into the water and its size is such

that when it touches the sides of the conical vessel, it is just

immersed. How much water will remain in the cone after the 

overflow? 

Solution :Let the radius of the spear=r and slant height of cone =h
Then r=A/S(The radius of a circle which is drawn inside a triangle) where A=area of trianle and S=semiperimeter of the triangle 
Here slant height=10cm
Area of trianle=48cm^2
Semiperimeter of the triangle=16cm
So radius=48/16=3cm
The left water content in the cone after submerging the spear=1/3x6^2x8-4/3x3^3=188.57cm^2(Answer)