Subjects geometry

Cube Net 64Fa0F

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

Question: Each of the figures below is made up of six squares. Three of the figures can be folded on the lines to form a cube. Which figure can not be folded into a cube?
1. **Problem Statement:** We have four figures, each made up of six squares. Three of these figures can be folded to form a cube, and one cannot. We need to identify which figure cannot be folded into a cube. 2. **Understanding Cube Nets:** A cube has 6 faces, each a square. A cube net is a 2D arrangement of 6 squares that can be folded into a cube. Important rules for cube nets: - The net must have exactly 6 squares. - The squares must be arranged so that when folded, each square corresponds to a face of the cube. - There are exactly 11 distinct nets for a cube. 3. **Analyzing Each Figure:** - **Figure 1:** Four squares in a horizontal row, with one square above the third square and one below the second square. This is a classic "T" shaped net, known to fold into a cube. - **Figure 2:** A stepped zigzag of six squares arranged in three rows, each shifted right. This shape is not one of the known cube nets because the squares are not connected in a way that allows folding into a cube. The zigzag arrangement prevents proper folding. - **Figure 3:** One square above the left square of a middle row of three squares, and two squares extending downward from the middle square. This is a known cube net shape and can fold into a cube. - **Figure 4:** Two squares on the top row, three squares on the middle row, and one square below the left square of the bottom. This arrangement matches one of the known cube nets. 4. **Conclusion:** The figure that cannot be folded into a cube is **Figure 2**. **Final answer:** Figure 2 cannot be folded into a cube.