# A cone,a hemisphere and a cylinder stand on equal bases and have the same height.Show that their volumes are in the ratio 1:2:3.

2
by nneehhaa66

2015-02-22T10:45:34+05:30
Let the radius of base be r

So the vol. of the cone =

Vol. of hemisphere=

Vol.of the cylinder: [/tex]

2015-02-22T10:50:05+05:30

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The formulas for the volumes of the solids are :

Cone:
V =  1/3 π R² H:   R = radius of the base  and   H  = the height of the cone
Base = π R²

Hemisphere:
V =  2/3 π  R³        , R = radius
Base = π R²

Cylinder :
V = π R² H     , R = radius  and  H is the height
Base = π R²

All of them have same base =>  Same Radius.   They have same height too.  The height of a hemisphere is same as the radius.  Hence,  R = H.

So ratio of their volumes =  1/3 π R² H : 2/3 π R³ :  π R² H
= H : 2 R : 3 H
= 1 : 2 : 3