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. 

Answer 1

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