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 :

Answer: Option B

Let the radius of a right circular cine be R cm and height be H cm
Volume of right circular cone $$=\frac{1}{3}\pi R^{2}H\text{ cu}\text{.cm}$$
When height of right circular cone is increased by 200% and radius of the base is reduce by 50%
New volume :
$$\begin{array}{rl}& \text{ = }\frac{1}{3}\pi {\left(\frac{R}{2}\right)}^2.3H\\ & =\frac{1}{3}\pi \frac{R^{2}4}{4}.3H\\ & =\frac{\pi R^{2}H}{4}\end{array}$$
Difference :
$$\begin{array}{rl}& =\pi R^{2}H\left(\frac{1}{3}-\frac{1}{4}\right)\\ & =\frac{1}{12}\pi R^{2}H\end{array}$$
Decrease percentage :
$$\begin{array}{rl}& =\frac{\frac{1}{12}\pi R^{2}H}{\frac{1}{3}\pi R^{2}H}\times 100\\ & =25\%\end{array}$$