r1 = 6cm
r2 = 8cm
r3 = 10cm
Volume of sphere = \(\frac{4}{3}\pi\,r^3\)
Volume of the resulting sphere = Sum of the volumes of the smaller spheres.
\(\frac{4}{3}\pi\,r^3\) = \(\frac{4}{3}\pi\,(r_1)^3\) + \(\frac{4}{3}\pi\,(r_2)^3\) + \(\frac{4}{3}\pi\,(r_3)^3\)
\(\frac{4}{3}\pi\,r^3\) = \(\frac{4}{3}\pi((r_1)^3+(r_2)^3+(r_3)^3)\)
r3 = 63 + 83 + 103
r3 = 1728
r = \(\sqrt[3]{1728}\)
r = 12 cm
Therefore, the radius of the resulting sphere is 12 cm.
