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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.

 Feb 20, 2020
 #1
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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

 

 

cool cool cool

 Feb 20, 2020

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