Determine the radius from the given diameter.

$$d = 7 \text{ cm}$$ $$r = \frac{d}{2} = \frac{7}{2} \text{ cm}$$

$$A = \pi r^2$$ $$A = \frac{22}{7} \times \left(\frac{7}{2} \text{ cm}\right)^2$$ $$A = \frac{22}{7} \times \frac{49}{4} \text{ cm}^2$$

$$A = \frac{22 \times 7}{4} \text{ cm}^2$$ $$A = \frac{154}{4} \text{ cm}^2$$ $$A = 38.5 \text{ cm}^2$$

The area of the circle is $\boxed{\text{38.5 cm}^2}$.

8. The area of a circle is 2464cm$^2$. Calculate its diameter to 2 sig. figures.

$$A = 2464 \text{ cm}^2$$ $$A = \pi r^2$$ $$2464 \text{ cm}^2 = \frac{22}{7} r^2$$

$$r^2 = \frac{2464 \times 7}{22} \text{ cm}^2$$ $$r^2 = \frac{17248}{22} \text{ cm}^2$$ $$r^2 = 784 \text{ cm}^2$$ $$r = \sqrt{784} \text{ cm}$$ $$r = 28 \text{ cm}$$

$$d = 2r$$ $$d = 2 \times 28 \text{ cm}$$ $$d = 56 \text{ cm}$$

The diameter is already 56 cm, which has two significant figures.
The diameter of the circle is $\boxed{\text{56 cm}}$.

9. Find the area of a semi circular field of diameter 20m.

$$d = 20 \text{ m}$$ $$r = \frac{d}{2} = \frac{20 \text{ m}}{2} = 10 \text{ m}$$

The area of a semi-circle is half the area of a full circle.

$$A_{semi} = \frac{1}{2} \pi r^2$$ $$A_{semi} = \frac{1}{2} \times \frac{22}{7} \times (10 \text{ m})^2$$ $$A_{semi} = \frac{1}{2} \times \frac{22}{7} \times 100 \text{ m}^2$$

$$A_{semi} = \frac{11}{7} \times 100 \text{ m}^2$$ $$A_{semi} = \frac{1100}{7} \text{ m}^2$$ $$A_{semi} \approx 157.14 \text{ m}^2$$

The area of the semi-circular field is $\boxed{\text{157.14 m}^2}$.

10. What is the diameter of a circle whose area is 154cm$^2$?

$$A = 154 \text{ cm}^2$$ $$A = \pi r^2$$ $$154 \text{ cm}^2 = \frac{22}{7} r^2$$

$$r^2 = \frac{154 \times 7}{22} \text{ cm}^2$$ $$r^2 = \frac{1078}{22} \text{ cm}^2$$ $$r^2 = 49 \text{ cm}^2$$ $$r = \sqrt{49} \text{ cm}$$ $$r = 7 \text{ cm}$$

$$d = 2r$$ $$d = 2 \times 7 \text{ cm}$$ $$d = 14 \text{ cm}$$

The diameter of the circle is $\boxed{\text{14 cm}}$.