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.
Ratio in volumes of two cones =4:5
and ratio of radii=2:3
Let radius of the first cone (r1)=2x
Then radius of second cone (r2)=3x
Let h1,h2be their heights respectively.
∴13πr21h1:13πr22h2=4:5⇒13πr21h113πr22h2=45⇒πr21h1πr22h2=45⇒(2x)2(3x)2×h1h2=45⇒4x29x2×h1h2=45⇒h1h2=45×9x24x2h1h2=95∴ Ratio between their vertical heights=9:5