The radius of two similar right circular cones are $2cm$ and $6cm$. The ratio of their volumes is

The correct option is D. $1:27$

Let radius of first cone be $r_1=2cm$ and that of the other radius be $r_2=6cm$.

Let height of the first height be $h_1$ and that of the other height be $h_2$.

Also, we know that, volume of cone is $\frac{1}{3}\pi r^{2}h$.

Since, the two cones are similar, therefore,

$\Rightarrow \frac{r_1}{r_2}=\frac{h_1}{h_1}$

$\Rightarrow \frac{2}{6}=\frac{h_1}{h_1}$

$\therefore \frac{h_1}{h_1}=\frac{1}{3}$

Hence, ratio of volume of two cones is,

$\Rightarrow \frac{\text{Volume of first cone}}{\text{Volume of second cone}}=\frac{\frac{1}{3}\pi r_1^2{h}_1}{\frac{1}{3}\pi r_2^2{h}_2}$

$=\frac{r_1^2{h}_1}{r_2^2{h}_2}$

$=\frac{(2{)}^2\times 1}{(6{)}^2\times 3}$

$=\frac{1}{27}$

Hence, the ratio of their volumes is $\frac{1}{27}$.