The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surface areas.

Given, ratio of slant height = 5 : 4 Let slant height of 1st cone be 5x cm and 2nd cone be 4x cm. For 1st cone, ⇒ Diameter = d 1 ⇒ Radius = r 1 ⇒ Slant height (l 1 ) = 5x For 2nd cone, ⇒ Diameter = d 2 ⇒ Radius = r 2 ⇒ Slant height (l 2 ) = 4x Given, ⇒ d 1 = d 2 ∴ r 1 = r 2 . Hence, ratio of curved surface areas = 5 : 4.