Volumes of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5. The ratio of their heights is:
Answer & explanation
Correct answer: option 4
Ratio of volumes of cones⇒ \(\frac{1}{3}\) \(\pi \)R12H1 : \(\frac{1}{3}\) \(\pi \)R22H2
⇒ R12H1 : R22H2 = 1 : 4 ...... (i)
Ratio of diameter = Ratio of radius = 4 : 5
In eq. (i)
⇒ R12H1 : R22H2 = 1 : 4
⇒ (4)2 H1 : (5)2 H2 = 1 :4
⇒ H1 : H2 = \(\frac{1}{4}\) × \(\frac{25}{16}\)
= 25 : 64