Q. 28

The surface area of a sphere and the curved surface area of a cylinder are in the ratio 2 : 1. Find the ratio of their volumes, if their radii are equal.

Answer :

Given the ratio of surface area of sphere
and curved surface area of cylinder = 4r: 2rh = 2 : 1 
(r is the common radius, and h is the height of the cylinder)
..     i.e. r = h
The ratio of the Volume of sphere and
Volume of cylinder =    (since h = r)   
                           =   
... Ratio of their volumes = 4 : 3

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