If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the cone :
Options:
A .  remains unaltered
B .  decreases by 25%
C .  increases by 25%
D .  increases by 50%
Answer: Option B Let the original radius and height of the cone be r and h respectively Then, Original volume = $$\frac{1}{3}\pi {r^2}h$$ New radius = $$\frac{r}{2}$$ and new hight = 2h New volume : $$\eqalign{ & = \frac{1}{3} \times \pi \times {\left( {\frac{r}{2}} \right)^2} \times 3h \cr & = \frac{3}{4} \times \frac{1}{3}\pi {r^2}h \cr} $$ ∴ Decrease % : $$\eqalign{ & = \left( {\frac{{\frac{1}{4} \times \frac{1}{3}\pi {r^2}h}}{{\frac{1}{3}\pi {r^2}h}} \times 100} \right)\% \cr & = 25\% \cr} $$
Submit Comment/FeedBack