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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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