Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
Diameter of a jar cylindrical in shape is increased by 25\%. By what percent must the height be decreased so that there is no change in its volume?
(a)10
(b)25
(c)36
(d)50
Answer
Answer (as printed): C
Explanation
Let original radius $=r$ and original height $=h$. Original volume $=\pi r^{2} h$. New radius $=125 \%$ of $r=\frac{5 r}{4}$. Let new height $=H$. Then, $\pi r^{2} h=\pi\left(\frac{5 r}{4}\right)^{2} \times H$ or $H=\frac{16}{25} h$. Decrease in height $=\left(h-\frac{16}{25} h\right)=\frac{9 h}{25}$. ∴ Decrease $\%=\left(\frac{9 h}{25} \times \frac{1}{h} \times 100\right) \%=36 \%$.
Explanation as extracted from the printed page; notation may be imperfect.