1. **Problem Statement:** Find the surface area of a solid formed by joining four cubes each with side length 25 cm in two different arrangements. 2. **Given:** Each cube has side length $s = 25$ cm. 3. **Formula for Surface Area of a Cube:** $$\text{Surface Area} = 6s^2$$ 4. **Step 1: Calculate surface area of one cube:** $$6 \times 25^2 = 6 \times 625 = 3750 \text{ cm}^2$$ 5. **Step 2: Arrangement 1 (T-shape 3D structure):** - Three cubes form the base layer in a row. - One cube is stacked on top of the center cube. 6. **Calculate total surface area for arrangement 1:** - Total surface area if separate: $4 \times 3750 = 15000$ cm$^2$ - But cubes share faces, so subtract the areas of shared faces. 7. **Shared faces in arrangement 1:** - Between the three cubes in the base: 2 shared faces, each $25 \times 25 = 625$ cm$^2$. - Between the top cube and the center base cube: 1 shared face, $625$ cm$^2$. 8. **Subtract shared faces twice (each shared face counted twice in total):** $$\text{Total shared area} = 3 \times 625 = 1875 \text{ cm}^2$$ 9. **Calculate surface area of arrangement 1:** $$15000 - 2 \times 1875 = 15000 - 3750 = 11250 \text{ cm}^2$$ 10. **Step 3: Arrangement 2 (2 by 2 flat square):** - Four cubes arranged in a square, one layer. 11. **Shared faces in arrangement 2:** - Each cube shares faces with adjacent cubes. - There are 4 shared faces between cubes (2 horizontal and 2 vertical), each $625$ cm$^2$. 12. **Total shared area:** $$4 \times 625 = 2500 \text{ cm}^2$$ 13. **Calculate surface area of arrangement 2:** $$15000 - 2 \times 2500 = 15000 - 5000 = 10000 \text{ cm}^2$$ 14. **Step 4: How does surface area change?** $$11250 - 10000 = 1250 \text{ cm}^2$$ The surface area decreases by 1250 cm$^2$ when rearranged from the T-shape to the 2 by 2 flat square. **Final answers:** - a) Surface area of T-shape solid: $11250$ cm$^2$ - b) Surface area of 2 by 2 flat square solid: $10000$ cm$^2$ - Surface area decreases by $1250$ cm$^2$ when rearranged.