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}