Answer:
Volume of the cone is [tex]\frac{1}{12}\pi r^{3}[/tex]
Step-by-step explanation:
Formula to find the volume of a cone is V = [tex]\frac{1}{3}\pi r^{2}h[/tex]
Here r is the radius of the cone and h is the height of the cone.
Since radius of cone = [tex]\frac{1}{2}(\text{Radius of cylinder})[/tex]
= [tex]\frac{r}{2}[/tex]
Height of the cone = radius of the cylinder = r
Now we put the values of radius and height of cone in the formula
Volume of cone = [tex]\frac{1}{3}\pi (\frac{r}{2})^{2}(r)[/tex]
= [tex]\frac{1}{3}\pi(\frac{r^{2}}{4})(r)[/tex]
= [tex]\frac{1}{12}\pi r^{3}[/tex]
Therefore, volume of the cone is [tex]\frac{1}{12}\pi r^{3}[/tex]
