Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A vertical cone of volume $V$ with vertex downwards is filled with water upto half of its height. The volume of the water is
(a)$\frac{V}{2}$
(b)$\frac{V}{4}$
(c)$\frac{V}{8}$
(d)$\frac{V}{16}$
Answer
Answer (as printed): C
Explanation
Let the radius and height of the cone be $r$ and $h$ respectively. Then, $V=\frac{1}{3} \pi r^{2} h$. Now, $\triangle A O B \sim \triangle C O D$. $$\text { ∴ Volume of water }=\frac{1}{3} \pi\left(\frac{r}{2}\right)^{2}\left(\frac{h}{2}\right)=\frac{1}{8}\left(\frac{1}{3} \pi r^{2} h\right)=\frac{V}{8} .$$
Explanation as extracted from the printed page; notation may be imperfect.