Question

The radius of a solid right circular cylinder increases by $20\%$ and its height decreases by $20\%$. Find the percentage change in its volume.

• A. $15.2$%
• B. $17.2$%
• C. $19.2$%
• D. $21.2$%

Answer 1

The correct option is A $15.2$%

Let initial height and radius of base of the cylinder be ${}^{\prime }{h}^{\prime }$ & ${}^{\prime }{r}^{\prime }$ respectively.

Now, initial volume, $V_1=\pi r^{2}h$

After increasing radius & decreasing height,

Final volume, $V_2=\pi {\left(1.2r\right)}^2\times \left(0.8h\right)=\pi r^{2}h\times 1.152$

% change in volume $=\frac{V_2-V_1}{V_1}\times 100=\frac{\pi r^{2}h(1.152-1)}{\pi r^{2}h}\times 100=15.2$%