Question

If the base radius and the height of a right circular cone are increased by 20 %,then the percentage increase in volume is approximately

• A. 60
• B. 68
• C. 73
• D. 78

Answer 1

The correct option is C

73

Let r be radius and h be height.

Initial volume, $V=\frac{1}{3}\pi r^{2}h$

By increasing the radius, new radius $r^{\prime }=r+\frac{20}{100}r=\frac{120}{100}r=\frac{6}{5}r$

New height, $h^{\prime }=\frac{6}{5}h$

New volume $V^{\prime }=\frac{1}{3}\pi (r^{\prime }{)}^2{h}^{\prime }=\frac{1}{3}\pi {\left(\frac{6}{5}r\right)}^2\times \left(\frac{6}{5}h\right)=\frac{1}{3}\pi \frac{36}{25}{r}^2\times \frac{6}{5}h=\frac{216}{125}\left(\frac{1}{3}\pi r^{2}h\right)=\frac{216}{125}V\therefore V^{\prime }=\frac{216}{125}V\therefore Increase=\frac{216}{125}V-V=\frac{216-125}{125}V=\frac{91}{125}VPercentageincrease=\frac{91}{125}V\times \frac{100}{V}=\frac{364}{5}\%=73\%(approx)$