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Answer :
Let r be the radius of the circle whose area is equal to the sum of the area of the circles of radii 8 cm and 6 cm.
\( \because \pi r^2 \ = \ \pi (8)^2 \ + \ \pi(6)^2 \)
\(\Rightarrow r^2 \ = \ 8^2 \ + \ 6^2 \)
\( \Rightarrow \ r^2 \ = \ 64 \ + \ 36 \ \)
\( \Rightarrow \ r \ = \ 10 \)
Hence, the radius of the new circle is 10 cm.