The radius of the large sphere = \(\frac{12}{2}\) cm = 6 cm. Now, the ratio of the diameters of the smaller spheres is 3 : 4 : 5 \[ \therefore \text{The radii of the smaller spheres are in the ratio } 3 : 4 : 5 \] Assume the radii of the smaller spheres are \(3r\) cm, \(4r\) cm, and \(5r\) cm respectively. According to the question: \[ \frac{4}{3}\pi(3r)^3 + \frac{4}{3}\pi(4r)^3 + \frac{4}{3}\pi(5r)^3 = \frac{4}{3}\pi(6)^3 \] Or, \[ 27r^3 + 64r^3 + 125r^3 = 216 \Rightarrow 216r^3 = 216 \Rightarrow r^3 = 1 \Rightarrow r = 1 \] \[ \therefore 3r = 3 \times 1 = 3 \text{ cm} \] \[ \therefore \text{Radius of the smallest sphere is } 3 \text{ cm} \]