ANSWER
[tex]0.314\operatorname{cm}[/tex]
EXPLANATION
The area of a sector is given as:
[tex]A=\frac{\theta}{360}\cdot\pi\cdot r^2[/tex]
where r = radius of the circle
θ = angle of the sector
From the question, we do not have the radius, but we have the diameter of the circle.
The diameter of a circle is twice its radius, which means that:
[tex]\begin{gathered} D=2\cdot r \\ r=\frac{D}{2} \\ r=\frac{2}{2} \\ r=1\operatorname{cm} \end{gathered}[/tex]
Therefore, the area of the sector is:
[tex]\begin{gathered} A=\frac{36}{360}\cdot\pi\cdot1^2 \\ A=0.314\operatorname{cm}^2 \end{gathered}[/tex]
