Question

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 1

The correct option is C $36\%$

Let radius be '$r$' and height of the jar be '$h$' respectively.
Volume $==\pi r^{2}h$
Increased radius $=1.25r$
Decreased height $H$ is given by $\pi r^{2}h=\pi {\left(1.25r\right)}^{2}H$
$\Rightarrow H=h\frac{16}{25}$
Percent decrease in height
$=\frac{9}{25}\times \frac{h}{h}\times 100=36$%