The problem in the image involves finding the area of the shaded region, which is the area between two concentric circles. We are given the radii of the two circles:

• Inner radius $r_{\text{inner}} = 80 \, \text{mm}$
• Outer radius $r_{\text{outer}} = 100 \, \text{mm}$

Step-by-step solution:

1. Area of the outer circle: $A_{\text{outer}} = \pi \times r_{\text{outer}}^2 = \pi \times (100)^2 = 10,000\pi \, \text{mm}^2$

2. Area of the inner circle: $A_{\text{inner}} = \pi \times r_{\text{inner}}^2 = \pi \times (80)^2 = 6,400\pi \, \text{mm}^2$

3. Area of the shaded region (difference between the outer and inner circle areas): $A_{\text{shaded}} = A_{\text{outer}} - A_{\text{inner}} = 10,000\pi - 6,400\pi = 3,600\pi \, \text{mm}^2$

Thus, the exact area of the shaded region is: $\boxed{3,600\pi} \, \text{mm}^2$

Would you like further details or explanations on any step?

Here are 5 related questions you might find helpful:

1. How do you calculate the area of a circle?
2. What is the concept of concentric circles?
3. How can you find the circumference of a circle given its radius?
4. What are some real-world applications of calculating areas between circles?
5. How does changing the radii affect the area of the shaded region?

Tip: When solving problems involving circular areas, always remember to work in terms of π when an exact answer is required!