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Question
The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2:3. Find the ratio of their vertical heights.
Solution
Let ratio of radius be 'r '
Radius of `1^(st)`cone = 2r
Radius of `2^(nd)`cone = 3r
Similarly
Let volume ratio be ‘v’
Volume of `1^(st)` cone→ 4v
Similarly volume of `2^(nd)` cone → 5v
∴`V_1/V_2=(4v)/(5v)=4/5`
⇒ `(1/3pir_1^2h_1)/(1/3pir_1^2)=4/5`
⇒`( h_1(2r)^2)/(h_2(3r)^2)=4/5`
⇒` h_1/h_2xx(4r^2)/(9r^2)=4/5`
⇒ `h_1/h_2xx36/20=18/20=9/5`
∴ Ratio of the inner height is 9:5
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