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 :

Solution(By Examveda Team)

Let original radius = r and original height = h
Original volume = $$\pi {r^2}h$$
New radius = 125% of r = $$\frac{5r}{4}$$
Let new height = H
Then,
$$\eqalign{ & \pi {r^2}h = \pi {\left( {\frac{{5r}}{4}} \right)^2} \times H \cr & Or,\,H = \frac{{16}}{{25}}h \cr} $$
Decrease in height :
$$\eqalign{ & = \left( {h - \frac{{16h}}{{25}}} \right) \cr & = \frac{{9h}}{{25}} \cr} $$
∴ Decrease % :
$$\eqalign{ & = \left( {\frac{{9h}}{{25}} \times \frac{1}{h} \times 100} \right)\% \cr & = 36\% \cr} $$