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Answer :
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.