Answer
5
Step-by-step explanation
The relationship between cylinder's radius, r, and cylinder's diameter, d, is:
[tex]r=\frac{d}{2}[/tex]
From the diagram, the diameter of the cylinder is 12 yards, then its radius is:
[tex]\begin{gathered} r=\frac{12}{2} \\ r=6\text{ yd} \end{gathered}[/tex]
The volume of the cylinder is calculated as follows:
[tex]V=\pi r^2h[/tex]
where h is the height of the cylinder.
Substituting V = 180π cubic yards, r = 6 yards, and solving for h:
[tex]\begin{gathered} 180\pi=\pi\cdot6^2\operatorname{\cdot}h \\ 180\pi=36\pi\operatorname{\cdot}h \\ \frac{180\pi}{36{}\pi}=\frac{36\pi\operatorname{\cdot}h}{36{}\pi} \\ 5\text{ yd}=h \end{gathered}[/tex]
