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A CONE,HEMISPHERE,CYLINDER, STAND ON EQUAL BASES AND HAVE SAME HEIGHT. SHOW THAT THE VOLUME ARE IN RATIO 1:2:3


Solution


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 
                        =  R³ :2 R³ : 3 R³
                        = 1 : 2 : 3
 

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