Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
If the height of a cone is doubled and its base diameter is trebled, then the ratio of the volume of the resultant cone to that of the original cone is
(a)6 : 1
(b)9 : 1
(c)9 : 2
(d)18 : 1
Answer
Answer (as printed): D
Explanation
Let the original radius and height of the cone be $r$ and $h$ respectively. Then, new radius $=3 r$ and new height $=2 h$. $$\therefore \frac{\text { New volume }}{\text { Original volume }}=\frac{\frac{1}{3} \times \pi \times(3 r)^{2} \times 3 h}{\frac{1}{3} \times \pi \times r^{2} \times h}=\frac{18}{1} .$$
Explanation as extracted from the printed page; notation may be imperfect.