A conical vessel of radius $12 cm$ and depth $16 cm$ is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the inner curved surface of the vessel, it is just immersed up to the topmost point of the sphere. How much water over flows out of the vessel out of the total volume $V$ cubic units?

The total volume V of the conical vessel is (1/3)πr^2h = (1/3)π(12)^2(16) = 768π. For the sphere to touch the sides and be exactly half-immersed, its radius R must be exactly half the cone's radius at the surface, so R = 6 cm. The volume of the submerged half of the sphere, which equals the volume of the overflowed water, is (1/2) times (4/3)π(6)^3 = 144π. By dividing the overflow volume by the total volume, we get 144π / 768π = 8/9, meaning 8/9 V of water overflows.

• Thanks
• Wrong explanation