This problem asks for the circumference and area of a circle with a radius of 8 km.

(a) Circumference: The formula for the circumference of a circle is: $C = 2 \pi r$ where $r$ is the radius.

Substituting $r = 8 \, \text{km}$: $C = 2 \pi (8) = 16 \pi \, \text{km}$

(b) Area: The formula for the area of a circle is: $A = \pi r^2$ Substituting $r = 8 \, \text{km}$: $A = \pi (8)^2 = 64 \pi \, \text{km}^2$

Summary:

• (a) Circumference = $16 \pi \, \text{km}$
• (b) Area = $64 \pi \, \text{km}^2$

Would you like further details or clarification? Here are some related questions you might find interesting:

1. How does changing the radius of a circle affect its circumference and area?
2. What is the relationship between the radius and the area of a circle?
3. How would the formula for the area of a circle change if the circle were an ellipse?
4. Can the formula for the circumference be used to calculate the area, and if so, how?
5. How would you approximate the value of $\pi$ to solve this problem numerically?

Tip: Always include $\pi$ in terms of a symbol if the problem asks for exact values, as it ensures precision.