Given data:
[tex]\begin{gathered} r=6\operatorname{cm} \\ \theta=60^{\circ} \end{gathered}[/tex]Area of sector of a circle is given by,
[tex]A=\frac{\theta}{360^{\circ}}\times2\pi r^2[/tex][tex]\begin{gathered} A=\frac{60}{360}\times2\times\frac{22}{7}\times6\times6 \\ \text{ =}\frac{1}{6}\times\frac{44}{7}\times6\times6 \end{gathered}[/tex][tex]A=\frac{264}{7}[/tex][tex]A=37.71[/tex]Thus, the area of sector is 37.71 cm square
[tex]\begin{gathered} A=\frac{60}{360}\times2\pi\times6\times6 \\ \text{ =}\frac{1}{6}\times2\pi\times36 \\ \text{ = 12}\pi \end{gathered}[/tex]
Thus, the answer is 12pi cm sq.