$a)\frac{\alpha }{{360}^o}\cdot 2\pi r=\frac{{\sout{{60}^o}}^1}{{\sout{{360}^o}}^6}\cdot 2\pi \cdot 4=\frac{1}{{\sout{6}}^3}\cdot {\sout{8}}^4\pi =\frac{4}{3}\pi =\underline{\underline{1\frac{1}{3}\pi }}$

$b)\frac{{\sout{{30}^o}}^1}{{\sout{{360}^o}}^{12}}\cdot 2\pi \cdot 6=\frac{1}{{\sout{12}}^1}\cdot {\sout{12\pi }}^{\pi }=\underline{\underline{\pi }}$

$c)\frac{{\sout{{270}^o}}^3}{{\sout{{360}^o}}^4}\cdot 2\pi \cdot 8=\frac{3}{{\sout{4}}^1}\cdot {\sout{16\pi }}^{4\pi }=\underline{\underline{12\pi }}$