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To solve this problem, let's go through it step-by-step.

### Problem Analysis:
1. We have identical small circles with a diameter of \(1 \, \text{cm}\).
2. These small circles are arranged inside a larger circle.
3. The task is to find the area of the shaded region between the large circle and the small circles.

### Solution Steps:

1. **Calculate the Radius of the Small Circles:**
   Since each small circle has a diameter of \(1 \, \text{cm}\), its radius \(r\) is:
   \[
   r = \frac{1}{2} = 0.5 \, \text{cm}
   \]

2. **Arrangement of the Small Circles in the Large Circle:**
   - In this configuration, 7 small circles fit inside the large circle: 6 around the perimeter and 1 in the center.
   - The 6 surrounding circles touch each other and the central circle.

3. **Calculate the Radius of the Large Circle:**
   - The distance from the center of the central small circle to the edge of one of the outer small circles is equal to 2 radii of the small circles (the central radius plus one outer radius).
   - Thus, the radius \(R\) of the large circle is:
     \[
     R = 2 \times 0.5 = 1 \, \text{cm}
     \]

4. **Calculate the Area of the Large Circle:**
   - The area \(A_{\text{large}}\) of the large circle with radius \(R = 1 \, \text{cm}\) is:
     \[
     A_{\text{large}} = \pi R^2 = \pi \times 1^2 = \pi \, \text{cm}^2
     \]

5. **Calculate the Area of One Small Circle:**
   - The area \(A_{\text{small}}\) of each small circle with radius \(r = 0.5 \, \text{cm}\) is:
     \[
     A_{\text{small}} = \pi r^2 = \pi \times (0.5)^2 = \frac{\pi}{4} \, \text{cm}^2
     \]

6. **Calculate the Total Area of the 7 Small Circles:**
   - Since there are 7 small circles, the total area of the small circles is:
     \[
     A_{\text{small total}} = 7 \times \frac{\pi}{4} = \frac{7\pi}{4} \, \text{cm}^2
     \]

7. **Calculate the Shaded Area:**
   - The shaded area is the difference between the area of the large circle and the total area of the small circles:
     \[
     A_{\text{shaded}} = A_{\text{large}} - A_{\text{small total}}
     \]
     \[
     A_{\text{shaded}} = \pi - \frac{7\pi}{4} = \frac{4\pi - 7\pi}{4} = -\frac{3\pi}{4}

Identical small circles with diameter 1 cm are inside a big one. Find the shaded area.

Learn how to find the shaded area when identical small circles with a diameter of 1 cm fit inside a larger circle. This solution covers geometric concepts, including circle area calculations and area subtraction. Suitable for students in Grades 9-10.

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