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.
Given the ratio of surface area of sphere
and curved surface area of cylinder = 4
r2 : 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
and curved surface area of cylinder = 4
r2 : 2rh = 2 : 1 (r is the common radius, and h is the height of the cylinder)
...
i.e. r = hThe ratio of the Volume of sphere and
Volume of cylinder =
(since h = r) =
... Ratio of their volumes = 4 : 3
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