Question

The radius of a right circular cone $A$ is $\frac{1}{5}$ of the radius of right circular cone $B$, and the height of right circular cone A is $\frac{1}{4}$ of the height of right circular cone B. Calculate the ratio of the volume of right circular cone A to the volume of right circular cone B.

• A. $\frac{1}{16}$
• B. $\frac{1}{25}$
• C. $\frac{1}{64}$
• D. $\frac{1}{80}$
• E. $\frac{1}{100}$

Answer 1

Answer: (E)

$\frac{1}{100}$

Let the radius of right circular cone $B$ is $r$ and height is $h$

Then radius of right circular cone $A$ is $\frac{1}{5}r$ and height is $\frac{1}{4}h$

Then volume of right circular cone $B=$ $\frac{1}{3}\pi r^{2}h$

andvolume of right circular cone $A=$$\frac{1}{3}\pi {\left(\frac{r}{5}\right)}^2\left(\frac{h}{4}\right)=\frac{1}{3}\times \frac{1}{25}\times \frac{1}{4}\pi r^{2}h$

Then ratio of volume $=$ $\frac{\frac{1}{3}\pi r^{2}h}{\frac{1}{3}\times \frac{1}{25}\times \frac{1}{4}\pi r^{2}h}=\frac{1}{100}$