Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
What is the ratio of the volume of the given right circular cone to the one obtained from it? I. The smaller cone is obtained by passing a plane parallel to the base and dividing the original height in the ratio 1 : 2. II. The height and the base of the new cone are one-third those of the original cone.
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
I. Let the radius and height of the bigger cone be $r$ and $h$ respectively and let its volume be $V_{1}$. Then, radius of smaller cone $=\frac{r}{2}$. And, height of smaller cone $=\frac{h}{2}$. Let the volume of the smaller cone be $V_{2}$. Then, $\frac{V_{1}}{V_{2}}=\frac{\frac{1}{3} \pi r^{2} h}{\frac{1}{3} \pi\left(\frac{r}{2}\right)^{2}\left(\frac{h}{2}\right)}=\frac{8}{1}$. Thus, I alone gives the answer. II. Let the radius and height of the bigger cone be $r$ and $h$ respectively and let its volume be $V_{1}$. Then, radius of smaller cone $=\frac{r}{3}$. And, height of smaller cone $=\frac{h}{3}$. Let the volume of the smaller cone be $V_{2}$. Then, $\frac{V_{1}}{V_{2}}=\frac{\frac{1}{3} \pi r^{2} h}{\frac{1}{3} \pi\left(\frac{r}{3}\right)^{2}\left(\frac{h}{3}\right)}=\frac{27}{1}$. Thus, II alone gives the answer. $\therefore$ Correct answer is (c).
Explanation as extracted from the printed page; notation may be imperfect.