Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

Sum of the volumes of 3 gives spheres.

\( = \ \frac{4}{3} \pi ((r_1)^3 \ + \ (r_2)^3 \ + \ (r_3)^3) \)

\(= \ \frac{4}{3} \pi (6^3 \ + \ 8^3 \ + \ 10^3) \)

\(= \ \frac{4}{3} \pi (216 \ + \ 512 \ + \ 1000) \)

\(= \ \frac{4}{3} \pi (1728) \) cm³

Let R be the radius of the new spheres whose volume is the sum of the volumes of 3 given spheres.

\( \Rightarrow \ \frac{4}{3} \pi R^3 \ = \ \frac{4}{3} \pi (1728) \)

\(\Rightarrow \ R^3 \ = \ 1728 \ => \ R \ = \ 12 \) cm

\(\therefore \) The radius of the resulting sphere is 12 cm.