The volume of a cone is given by the formula:
[tex]V=\frac{1}{3}\times\pi\times h\times r^2[/tex]
Where r is the radius of the base of the cone and h is its height.
From this equation, we can solve for h like this:
[tex]\begin{gathered} V=\frac{1}{3}\pi hr^2 \\ \frac{V}{\pi r^2}\times3=\frac{1}{3}\frac{\pi hr^2}{\pi r^2}\times3 \\ \frac{3V}{\pi r^2}=\frac{3}{3}\frac{\pi r^2}{\pi r^2}h \\ h=\frac{3V}{\pi r^2} \end{gathered}[/tex]
Now let's replace the values that we know into this formula
V=91185.6 yd^3
r=44 yd
[tex]\begin{gathered} h=\frac{3V}{\pi r^2} \\ h=\frac{3\times91185.6}{3.14\times44^2}=45 \end{gathered}[/tex]
Then, the height of the cone equals 45 yards
