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:
Answer & explanation
Correct answer: option 1
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