A conical vessel of radius 6cm and height 8cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed as shown in the figure. What fraction of water flows out.

Ans:    This problem can be done in many ways

Let "r" be the radius of sphere

In right triangle

Tan θ = 6/8 = 3/4

=> Sin θ =  3/5

in rt Δ

Sin θ = r/VO    = 3/5 =r/8 - r

r = 3 cm

Volume of H2 O that flows out of cone = volume of sphere fraction of water Overflows = volume f sphere/Volume of cone

= 36 π/96 π = 3/8