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  3. The base radii of two right circular cones of the same height are in the ratio 3: 5 . Find the ratio of their volumes .
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The base radii of two right circular cones of the same height are in the ratio 3: 5 . Find the ratio of their volumes .

Answers (1)
D Deependra Verma

Solution: Let r_1 and r_2 be the radii of two cones and V_1 and V_2 be their volumes . Let h be the height of the two cones . 

                Then, 

                        V_1= frac13pi r^2_1h    and    V_2= frac13pi r^2_2h

herefore                     fracV_1V_2=fracfrac13 pi r^2_1hfrac13pi r^2_2h=fracr^2_1r^2_2=frac925                                              [ecause fracr_1r_2=frac35 (Given) herefore fracr^2_1r^2_2=frac925]

Hence the ratio of the volume of two cones is 9 : 25 . 

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