Question

If the base radius and the height of a right circular cone are increased by $40\%$, then find the percentage increase in volume (approx).

Answer 1

Let initial radius, height, volume and final radius, height, volume be $r,h,v$ and $R,H,V$, respectively.

Then, $R=r+0.4r=1.4r$ & $H=h+0.4h=1.4h$.

$\Rightarrow V=\frac{\pi }{3}{R}^2{H}^2=\left(\frac{\pi }{3}{r}^{2}h\right)(1.4{)}^3=2.744v$.

$\therefore$ increase $\%$ in volume $=\frac{V-v}{v}\times 100$

$=\frac{2.744v-v}{v}\times 100$

$=1.744\times 100=174.4\%$.