https://file.aiquickdraw.com/mathbot/file/172948630099892ysdo32.jpg

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!

Find the area of the shaded region between two concentric circles with an inner radius of 80 mm and an outer radius of 100 mm. Express your answer in terms of π.

Learn how to calculate the area of a shaded region between two concentric circles with an inner radius of 80 mm and an outer radius of 100 mm. Follow the step-by-step solution, which includes the use of the circle area formula and exact answers in terms of π.

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