To solve this problem, we need to calculate the surface area of the 3D solid formed by smaller 1 cm³ cubes.

Step-by-Step Solution

1. Analyze the Structure: The image shows a cube structure composed of smaller cubes. Each smaller cube has a side length of 1 cm.

2. Dimensions of the Solid: From the image, it seems the solid is a $3 \times 3 \times 3$ cube, meaning there are 3 cubes along each dimension.

3. Total Surface Area Calculation: The surface area of a cube is calculated using the formula: $\text{Surface Area} = 6 \times \text{side}^2$ However, since we are dealing with a larger $3 \times 3 \times 3$ cube, we need to calculate the surface area for this composite structure.

4. Surface Area of the Larger Cube: The larger cube has a side length of 3 cm, so: $\text{Surface Area} = 6 \times (3 \, \text{cm})^2 = 6 \times 9 \, \text{cm}^2 = 54 \, \text{cm}^2$

Thus, the surface area of the given solid is $54 \, \text{cm}^2$.

Do you have any questions or would you like further details?

Related Questions

1. How would the surface area change if the cube were $4 \times 4 \times 4$?
2. What is the volume of this $3 \times 3 \times 3$ cube?
3. How does the surface area of a cube change with respect to its side length?
4. How many smaller 1 cm³ cubes are there in this $3 \times 3 \times 3$ structure?
5. What would be the surface area if only one side of the larger cube were visible?

Tip

For composite shapes, it's often helpful to consider both the larger structure and the individual smaller components for calculations.