Answer: B
The radius of the large sphere = \(\frac{12}{2}\) cm = 6 cm Now, the diameters of the smaller spheres are in the ratio 3 : 4 : 5 \(\therefore\) The radii of the smaller spheres are also in the ratio 3 : 4 : 5 Let the radii of the smaller spheres be \(3r\) cm, \(4r\) cm, and \(5r\) cm respectively \(\therefore\) According to the question, \[ \frac{4}{3}\pi (3r)^3 + \frac{4}{3}\pi (4r)^3 + \frac{4}{3}\pi (5r)^3 = \frac{4}{3}\pi (6)^3 \] i.e., \[ 27r^3 + 64r^3 + 125r^3 = 216 \] \[ 216r^3 = 216 \] \[ r^3 = 1 \] \[ r = 1 \] \(\therefore\) The radius of the smallest sphere is \(3r = 3\) cm.
The radius of the large sphere = \(\frac{12}{2}\) cm = 6 cm Now, the diameters of the smaller spheres are in the ratio 3 : 4 : 5 \(\therefore\) The radii of the smaller spheres are also in the ratio 3 : 4 : 5 Let the radii of the smaller spheres be \(3r\) cm, \(4r\) cm, and \(5r\) cm respectively \(\therefore\) According to the question, \[ \frac{4}{3}\pi (3r)^3 + \frac{4}{3}\pi (4r)^3 + \frac{4}{3}\pi (5r)^3 = \frac{4}{3}\pi (6)^3 \] i.e., \[ 27r^3 + 64r^3 + 125r^3 = 216 \] \[ 216r^3 = 216 \] \[ r^3 = 1 \] \[ r = 1 \] \(\therefore\) The radius of the smallest sphere is \(3r = 3\) cm.