1. **Problem 18:** For each net of a cube, determine which face is opposite face 1 when folded. 2. **Understanding cube nets:** A cube has 6 faces, and opposite faces sum to 7 in standard numbering. We analyze each net's layout to find the face opposite to face 1. 3. **Net A:** Layout: - Top row: 2, 3, 4 - Below 3: 5 - Below 5: 6 - Right of 4: 1 When folded, face 1 is adjacent to 4 and 3, so the face opposite 1 is 5. 4. **Net B:** Layout: 6, 4, 1, 2, 3, 5 in a line. Face 1 is in the middle, adjacent to 4 and 2. The faces 6 and 5 are at the ends and opposite to 1. By folding, face 6 is opposite to 1. 5. **Net C:** Layout: L-shape with 2,3,4,5,6 vertically below 1. Face 1 is at the top right, adjacent to 2 and 6. The face opposite 1 is 4. --- 6. **Problem 19:** Given a cube of side length $x$ cm, volume equals surface area numerically. 7. **Formulas:** - Volume $V = x^3$ - Surface area $S = 6x^2$ Given $V = S$, so: $$x^3 = 6x^2$$ 8. **Solve the equation:** $$x^3 = 6x^2$$ Divide both sides by $x^2$ (assuming $x \neq 0$): $$\cancel{x^3}^{x^2} = 6\cancel{x^2}^{x^2} \implies x = 6$$ 9. **Check solution:** - Volume: $6^3 = 216$ - Surface area: $6 \times 6^2 = 6 \times 36 = 216$ Both equal, so $x = 6$ cm. **Final answers:** - Net A: Opposite face to 1 is 5 - Net B: Opposite face to 1 is 6 - Net C: Opposite face to 1 is 4 - Cube side length $x = 6$ cm