Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then the ratio of their heights will be
(a)3 : 4
(b)4 : 3
(c)3 : 8
(d)8 : 3
Answer
Answer (as printed): D
Explanation
Let their radii be $x$ and $2 x$, and their heights be $h$ and $H$ respectively. Then, $$\frac{\frac{1}{3} \times \pi \times x^{2} \times h}{\frac{1}{3} \times \pi \times(2 x)^{2} \times H}=\frac{2}{3} \quad \text { or } \quad \frac{h}{H}=\frac{2}{3} \times 4=\frac{8}{3} .$$
Explanation as extracted from the printed page; notation may be imperfect.