Step 1: Spot the odd statement first:
Three of the statements are standard results, but statement (A) talks about volume. Volume belongs to solid shapes such as a sphere or a cone. A circle drawn on paper is a flat shape, so it has no volume.
Step 2: Confirm (A) is false:
Even if we treated $\frac{2}{3}\pi r^2$ as an area, the area of a circle is $\pi r^2$, and $\frac{2}{3}\pi r^2$ is not that. So (A) fails on both counts.
Step 3: Confirm the rest with a test case:
Take $r = 1$ and $\theta = 360$ degrees.
Circumference: $2\pi(1) = 2\pi$, which matches (B).
Area: $\pi(1)^2 = \pi$, which matches (C).
Sector area: $\frac{\pi \cdot 1 \cdot 360}{360} = \pi$, the full circle, which matches (D).
Step 4: Also test a half circle:
Take $\theta = 180$. Then (D) gives $\frac{\pi r^2}{2}$, half the circle. This is right, so (D) holds for other angles too.
Final Answer:
Only (B), (C) and (D) are correct, which is option (2).
\[ \boxed{\text{(B), (C), (D) only}} \]