Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
$X$ and $Y$ are two cylinders of the same height. The base of $X$ has diameter that is half the diameter of the base of $Y$. If the height of $X$ is doubled, the volume of $X$ becomes
(a)equal to the volume of $Y$
(b)double the volume of $Y$
(c)half the volume of $Y$
(d)greater than the volume of $Y$
Answer
Answer (as printed): C
Explanation
Let the height of $X$ and $Y$ be $h$, and their radii be $r$ and $2 r$ respectively. Then, Volume of $X=\pi r^{2} h$ and Volume of $Y=\pi(2 r)^{2} h=4 \pi r^{2} h$. New height of $X=2 h$. So, new volume of $X$ $$=\pi r^{2}(2 h)=2 \pi r^{2} h=\frac{1}{2}\left(4 \pi r^{2} h\right)=\frac{1}{2} \times(\text { Volume of } Y) .$$
Explanation as extracted from the printed page; notation may be imperfect.