Answer :
We can write the volume of the cylinder as the product of the area of the base and its height:
[tex]V=A_b\cdot h[/tex]The area of the base is:
[tex]A_b=\pi r^2[/tex]Then, we can write the first equation and clear the height as:
[tex]\begin{gathered} V=A_b\cdot h=\pi r^2\cdot h \\ h=\frac{V}{\pi r^2} \end{gathered}[/tex]Replcing with the values V=180 cm^3 and r=3 cm, we get:
[tex]h=\frac{180\operatorname{cm}^3}{\pi\cdot(3\operatorname{cm})^2}=\frac{180\operatorname{cm}^3}{\pi\cdot9\operatorname{cm}}\approx\frac{180\operatorname{cm}^3}{28.3\operatorname{cm}^2}=6.4\operatorname{cm}[/tex]Answer: the height is 6.4 cm.