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If the volume of two right circular cones are in the ratio 1 : 3 and their diameters are in the ratio 3 : 5, then the ratio of their heights is ?
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- 25 : 27
- 1 : 5
- 3 : 5
- 5 : 27
Correct Option: A
Let diameter, radius and height of first cone are d1, r1 and h1, respectively and that of second cone are d2, r2 and h2, respectively.
r1/r2 = d1/d2 = 3/5,
h1/h2 = ?
Given,
[(1/3)πr21h1] / [(1/3)πr22h2] = 1/3
⇒ (3/5)2 x h1/h2 = 1/3
⇒ h1/h2 = (1/3) x (25/9) = 25/27
