1. **State the problem:** We need to find the area of a sector of a circle with radius $r=5$ cm and central angle $\theta=30^\circ$. Also, complete the statement about the diameter and radius of a circle. 2. **Formula for the area of a sector:** The area $A$ of a sector with radius $r$ and angle $\theta$ (in degrees) is given by: $$A = \frac{\theta}{360} \times \pi r^2$$ 3. **Calculate the area:** Substitute $r=5$ cm and $\theta=30^\circ$: $$A = \frac{30}{360} \times \pi \times 5^2 = \frac{1}{12} \times \pi \times 25 = \frac{25\pi}{12}$$ 4. **Answer in terms of $\pi$:** $$A = \frac{25\pi}{12} \text{ cm}^2$$ 5. **Complete the statement:** For any circle, the diameter is **2** times the radius. This means: $$\text{diameter} = 2 \times \text{radius}$$