Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A fountain having the shape of a right circular cone is fitted into a cylindrical tank of volume V so that the base of the tank coincides with the base of the cone and the height of the tank is the same as that of the cone. The volume of water in the tank, when it is completely filled with water from the fountain, is
(a)$\frac{V}{2}$
(b)$\frac{V}{3}$
(c)$\frac{V}{4}$
(d)$\frac{2 V}{3}$
Answer
Answer (as printed): D
Explanation
Let the radius and height of the tank be $r$ and $h$ respectively. Then, $V=\pi r^{2} h$. ∴ Volume of water in the tank = Vol. of cylinder - Vol. of cone $$=\pi r^{2} h-\frac{1}{3} \pi r^{2} h=\frac{2}{3} \pi r^{2} h=\frac{2}{3} V .$$
Explanation as extracted from the printed page; notation may be imperfect.