$\text{Volume Cone}=\frac{1}{3}\pi {r}^{2}h$
$\text{Volume Sphere}=\frac{4}{3}\pi {r}^{3}$
$\text{Volume Cylinder}=\pi {r}^{2}h$
$\text{where}r\text{is the radius and}h\text{is the height}$

First, use the formula for the volume of a sphere to find the radius.

$\begin{array}{rcl}\text{Volume}& =& \frac{4}{3}\pi {r}^{3}\\ 113.04{\text{cm}}^{3}& =& \frac{4}{3}\pi {r}^{3}\\ 113.04{\text{cm}}^{3}& =& \frac{4}{3}\text{(}3.14\text{)}{r}^{3}\\ 113.04{\text{cm}}^{3}\xf73.14& =& \frac{4}{3}\text{(}3.14\text{)}{r}^{3}\xf73.14\\ 36{\text{cm}}^{3}& =& \frac{4}{3}{r}^{3}\\ 36{\text{cm}}^{3}\times \frac{3}{4}& =& \frac{4}{3}{r}^{3}\times \frac{3}{4}\\ 27{\text{cm}}^{3}& =& {r}^{3}\\ 3\text{cm}& =& r\end{array}$

The radius is 3 centimeters. So, the diameter is 6 centimeters.