we can use
volume of cone formula
[tex]V=\frac{1}{3} \pi r'^2 h'[/tex]
where
r' is radius of cone
h' is height of cone
we are given
The radius of the cone is half the radius of the cylinder
so,
[tex]r'=\frac{r}{2}[/tex]
The height of the cone is equal to the radius of the cylinder
so,
[tex]h'=r[/tex]
now, we can plug values into formula
we get
[tex]V=\frac{1}{3} \pi (\frac{r}{2})^2*r[/tex]
we can simplify it
[tex]V=\frac{1}{12} \pi r^3[/tex]
so, option-C.........Answer
