If the ratio of the volumes of two cones is 11:16 and the ratio of the radii of their bases is 3:4, then the ratio of their heights will be:

11 : 9 4 : 11 3 : 16 9 : 11

11 : 9

Volume of cone = \(\frac{1}{3}\)\(\Pi \)\( {r }^{2 } \)h Ratio of volume = 11 : 16 ⇒ R  :  H    3  :  4    3  :  4    h1: h2 9 h1 : 16h2 = Volume ⇒ 9 H1 = 11   ,  16 H2 = 16 ⇒ H1 = \(\frac{11}{9}\)   H2 = 1 ⇒ H1 : H2 = 11 : 9