Question

The diameter of a right circular cylinder increases by $50$% and its height decreases by $40$% then finds the percentage change in its volume.

• A. $30$% increase
• B. $35$% increase
• C. $40$% increase
• D. None of these

Answer 1

Answer: (B)

$35$% increase

Given, a right circular cylinder with diameter $d$,radius $r$, and height $h$

Volume of cylinder$=\pi r^{2}h$

Diameter is increased by $50\%$, so radius is also increased by $50\%$ $=r+$ $0.5$ $r$ $=1.5$ $r$

Height is decreased by $40\%$ $=h-$ $0.4$ $h$ $=0.6$ $h$

New Volume$=\pi r^{2}h$

$=\pi \times {\left(1.5r\right)}^2\times 0.6h$

$=1.35\pi r^{2}h$

The new volume is greater than the previous volume.

So, volume is increased.

$\%$ increased $=\frac{Newvolume-volume}{Volume}\times 100$%

$=\frac{1.35\pi r^{2}h-\pi r^{2}h}{\pi r^{2}h}\times 100$%

$=\frac{0.35\pi r^{2}h}{\pi r^{2}h}\times 100$%

$=35$ $\%$