The volume of a cone is computed as follows:
[tex]V\text{ of cone}=\pi r^2\frac{h}{3}[/tex]
where r is the radius and h is the height of the cone.
The volume of a cylinder is computed as follows:
[tex]V\text{ of cylinder=}\pi r^2h[/tex]
where r is the radius and h is the height of the cylinder.
Substituting with r = 1 and h = 1, the volumes are:
[tex]\begin{gathered} V\text{ of cone}=\pi\cdot1^2\cdot\frac{1}{3}=\pi\cdot1\cdot\frac{1}{3}\approx1.05 \\ V\text{ of cylinder=}\pi\cdot1^2\cdot1=\pi\approx3.14 \end{gathered}[/tex]
And the ratio of volumes is:
[tex]\frac{V\text{ of cone}}{V\text{ of cylinder }}=\frac{1.05}{3.14}\approx0.33[/tex]
Substituting with r = 2 and h = 4, the volumes are:
[tex]\begin{gathered} V\text{ of cone}=\pi\cdot2^2\cdot\frac{4}{3}=\pi\cdot4\cdot\frac{4}{3}\approx16.76 \\ V\text{ of cylinder=}\pi\cdot2^2\cdot4=\pi\cdot4\cdot4\approx50.26 \end{gathered}[/tex]
And the ratio of volumes is:
[tex]\frac{V\text{ of cone}}{V\text{ of cylinder }}=\frac{16.76}{50.26}\approx0.33[/tex]
