SOLUTION
The radius of the cone is half the radius of the cylinder.
Let r be the radius of cylinder
Then the radius of cone is
[tex]r_c=\frac{r}{2}[/tex]
The height of the cone is equal to the radius of the cylinder
Hence the height of the cone is
[tex]h_c=r[/tex]
The formula for volume of a cone is given as:
[tex]V=\frac{1}{3}\pi r_c^2h_c[/tex]
Substitute the radius and height of cone into the formula
[tex]\begin{gathered} V=\frac{1}{3}\pi(\frac{r}{2})^2r \\ V=\frac{1}{3}\frac{\pi r^3}{4} \\ V=\frac{1}{12}\pi r^3 \end{gathered}[/tex]
Therefore the required volume is
[tex]V=\frac{1}{12}\pi r^3[/tex]
