According to the question it is given that,
Radius of the copper sphere $=3cm$
As we know that,
Volume of the sphere $=4/3\pi {{r}^{3}}$
$=4/3\pi \times {{3}^{3}}$ ….. (i)
The copper sphere is melted and recasted into a right circular cone
Height of the cone $=3cm$
As we know that,
Volume of the right circular cone $=1/3\pi {{r}^{2}}h$
$=1/3\pi \times {{r}^{2}}\times 3$….. (ii)
On comparing equation (i) and (ii) we have,
$4/3\pi \times {{3}^{3}}=1/3\pi \times {{r}^{2}}\times 3$
${{r}^{2}}=36$
$r=6cm$
Therefore, the radius of the base of the cone is $6cm$.