Let the radius and height of cone be r and h respectively
\[Radius\text{ }of\text{ }sphere\text{ }=\text{ }R\]
\[{{R}^{2}}~=\text{ }{{r}^{2}}~+\text{ }{{\left( h\text{ }-\text{ }R \right)}^{2}}\]
\[{{R}^{2}}~=\text{ }{{r}^{2}}~+\text{ }{{h}^{2}}~+\text{ }{{R}^{2}}-\text{ }2hR\]
\[{{r}^{2}}~=\text{ }2hR\text{ }-\text{ }{{h}^{2}}~\ldots \text{ }\left( 1 \right)\]
Assuming volume of cone be $V$
