A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A metal sphere is now lowered into the water. The size of the sphere is such that when it touches the inner surface, it just gets immersed. Find the fraction of water that overflows from the conical vessel.
+128407 See the following image :
The cone's radius = BC and the height is AB
If we find the intersection of the angle bisectors, we will have the center of the sphere....this is at E = (0,5)
From the image....the radius of this sphere = BE = 3
The volume of the cone is (1/3) pi ( r^2) * h = (1/3) pi * 6^2 * 8 = 96 pi cm^3
And the volume of the sphere will = the spillage amount = (4/3) pi (r^3) = (4/3) pi (3)^3 =
36 pi cm^3
So.....the fraction of the water that spills out =
36 pi 3
____ = __
96 pi 8
