Verified Answer :

\(The\ volume\ of\ the\ cube:V=a^3\ (a-length\ of\ an\ edge)\\\\V=343 cm^3\to a^3=343cm^3\to a=\sqrt[3]{343cm^3}\to \boxed{a=7cm}\\\\because\ 7^3=343\\-------------------------------\\\\the\ surface\ area\ of\ the\ cube:A_S=6a^2\\\\therefore\\\\A_S=6\cdot7^2=6\cdot49=\boxed{294\ (cm^2)}\)

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\(\rm The~side~of~the~cube:~\bold{S} \\ \\ V=343 \\ \\ S^3=343 \\ \\ S= \sqrt[3]{343} \\ \\ S=7~cm \\ \\ A=6*A^2 \\ \\ A=6*7^2 \\ \\ A=6*49 \\ \\ \bold{\underline{A=294~cm^2}}\)