Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50\% more than its height. If the diameter is same for both the bowl and the cylinder, the volume of the beverage in the cylindrical vessel is
(a)$66 \frac{2}{3} \%$
(b)$78 \frac{1}{2} \%$
(c)100\%
(d)More than 100\% (i.e., some liquid will be left in the bowl)
Answer
Answer (as printed): C
Explanation
Let the height of the vessel be $x$. Then, radius of the bowl $=\text{radius of the vessel}=\frac{x}{2}$. Volume of the bowl, $V_{1}=\frac{2}{3} \pi\left(\frac{x}{2}\right)^{3}=\frac{1}{12} \pi x^{3}$. Volume of the vessel, $V_{2}=\pi\left(\frac{x}{2}\right)^{2} x=\frac{1}{4} \pi x^{3}$. Since $V_{2}>V_{1}$, so the vessel can contain 100\% of the beverage filled in the bowl.
Explanation as extracted from the printed page; notation may be imperfect.