Question

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 is:

• A. Remain unaltered
• B. Decreases by 25%
• C. Increases by 25%
• D. Increases by 50%
• E. Decreased by 45%

Answer 1

The correct option is B

Decreases by 25%

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 height = 3h

New volume $=\frac{1}{3}\times \pi \times {\left(\frac{r}{2}\right)}^2\times 3h=\frac{3}{4}\times \frac{1}{3}\pi r^{2}h$

$\therefore$Decrease % = $\left(\frac{\frac{1}{4}\times \frac{1}{3}\pi r^{2}h}{\frac{1}{3}\pi r^{2}h}\times 100\right)$