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 \(\therefore\) The ratio of the radii of the smaller spheres is also 3 : 4 : 5 Let the radii of the smaller spheres be \(3r\) cm, \(4r\) cm, and \(5r\) cm respectively According to the question: \[ \frac{4}{3}\pi (3r)^3 + \frac{4}{3}\pi (4r)^3 + \frac{4}{3}\pi (5r)^3 = \frac{4}{3}\pi (6)^3 \] Simplifying: \[ 27r^3 + 64r^3 + 125r^3 = 216 \] \[ 216r^3 = 216 \] \[ r^3 = 1 \] \[ r = 1 \] \(\therefore\) The radii of the smaller spheres are 3 cm, 4 cm, and 5 cm respectively.