Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A conical flask has base radius $a \mathrm{cm}$ and height $h$ cm. it is completely filled with milk. The milk is poured into a cylindrical thermos flask whose base radius is $p$ cm. What will be the height of the milk level in the flask?
(a)$\frac{a^{2} h}{3 p^{2}} \mathrm{cm}$
(b)$\frac{3 h p^{2}}{a^{2}} \mathrm{cm}$
(c)$\frac{p^{2}}{3 h^{2}} \mathrm{cm}$
(d)$\frac{3 a^{2}}{h p^{2}} \mathrm{cm}$
Answer
Answer (as printed): A
Explanation
Volume of milk in conical flask $=\left(\frac{1}{3} \pi a^{2} h\right) \mathrm{cm}^{3}$. Let the height of the milk in the cylindrical flask be $x \mathrm{cm}$. Then, volume of milk in cylindrical flask $=\left(\pi p^{2} x\right) \mathrm{cm}^{3}$. $$\therefore \frac{1}{3} \pi a^{2} h=\pi p^{2} x \Rightarrow x=\frac{1}{3} \frac{\pi a^{2} h}{\pi p^{2}}=\frac{a^{2} h}{3 p^{2}} \mathrm{cm} .$$