Pole inside the cube

Since total surface area of cube= $6{ a }^{ 2 }$ . We get the equation $6{ a }^{ 2 }=216$ . On solving, we get $a=6$ . Length of the longest rod = $\sqrt [ ]{ { 6 }^{ 2 }+{ 6 }^{ 2 }+{ 6 }^{ 2 } }$ = $6\sqrt { 3 }$

Given:

Total surface area $=6a^{2}=216$

$a^{2}=36$

$a=6$ cm

Length of the longest rod (Diagonal) $=\sqrt{a^{2}+a^{2}+a^{2}}$

$=\sqrt{3a^{2}}=a\sqrt{3}=6\sqrt{3}$ cm

Thus, the answer is: $a=\boxed{6\sqrt{3}}$