Answer :
The volume of a right circular cone is given by
[tex]V=\frac{1}{3}\pi r^2h[/tex]Since we know the diameter of the base is 6.6 cm, then the radio its the half of it, that is, 3.3 cm. we also know the volume, plugging the values we know into the equation we have
[tex]54.45\pi=\frac{1}{3}\pi(3.3)^2h[/tex]Solving for h:
[tex]\begin{gathered} 54.45\pi=\frac{1}{3}\pi(3.3)^2h \\ \frac{(3)(54.45\pi)}{(3.3)^2\pi}=h \\ \frac{163.35}{10.89}=h \\ h=15 \end{gathered}[/tex]Therefore the height of the cone is 15.