Question

If the radius of the base of a right circular cone is halved keeping the height same then the ratio of the volume of the reduced cone to that of the original cone is

• A. 2 : 1
• B. 4 : 1
• C. 1 : 4
• D. 1 : 2

Answer 1

Answer: (B)

Let the radius and height of right circular cone

Then volume $V_1=\pi r^{2}h$

If radius is half of radius =$\frac{r}{2}$ and height =h

Then volume $V_2=\pi (\frac{r}{2}{)}^{2}h=\frac{\pi r^{2}h}{4}$

Then ratio $V_1:V_2=\pi r^{2}h:\frac{\pi r^{2}h}{4}=4:1$