Since the diameter of the larger sphere is twice that of the smaller sphere, \(\therefore\) the radius of the larger sphere will be twice the radius of the smaller sphere. Let the radius of the smaller sphere be \(r\) units. \(\therefore\) the radius of the larger sphere is \(2r\) units. According to the question: \[ 4\pi (2r)^2 = \frac{4}{3}\pi r^3 \Rightarrow 4r^2 = \frac{r^3}{3} \Rightarrow r^3 = 12r^2 \Rightarrow r = 12 \] Therefore, the radius of the smaller sphere is 12 units.