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A cone is divided into two

parts by drawing a plane through the midpoint of its axis, parallel to its
base. Compare the volumes of two parts.



the actual volume of cone is 1/3R^2H.
and after the cone is cut the top part which is the small cone ,its volume is 1/3πr^2h.
and now the volume of frustum of a cone which is the part left after the small cone above is cut is 1/3πR^2H-1/3πr^2h.
             as the cone is cut exactly at the centre of axis,h=H/2 so the ratio of two volumes will be,
(1/3πr^2H/2)/1/3πR^2H-1/3r^2H/2=r^2/2R^2-r^2 .
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