Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2009 · Marks: · Difficulty:
If the heights of two cones are in the ratio 7 : 3 and their diameters are in the ratio 6 : 7, what is the ratio of their volumes?
(a)3 : 7
(b)4 : 7
(c)5 : 7
(d)12 : 7
Answer
Answer (as printed): D
Explanation
Let the heights of two cones be $7 x$ and $3 x$ and their radii be $6 y$ and $7 y$ respectively. Then, $$\text { Ratio of volumes }=\frac{\frac{1}{3} \pi \times(6 y)^{2} \times 7 x}{\frac{1}{3} \pi \times(7 y)^{2} \times 3 x}=\frac{36 \times 7}{49 \times 3}=\frac{12}{7} \text {. }$$
Explanation as extracted from the printed page; notation may be imperfect.