Final answer:
The ratio of the surface area of the larger 10 cm side block of wood to the combined surface area of the smaller 1 cm side blocks that it is cut into is 1:10.
Step-by-step explanation:
The student has asked for the ratio of the surface area of a larger block of wood to the combined surface area of smaller blocks of wood resulting from cutting the larger block. To find this, we must first calculate the surface area of both the larger cube and the smaller cubes.
Larger Cube:
Side length: 10 cm
Surface area (SA) = 6 × side length² = 6 × 10² = 600 cm²
Smaller Cubes:
Side length: 1 cm
Each cube has a surface area of 6 cm² since SA = 6 × side length² = 6 × 1².
The larger cube can be cut into 10³ = 1000 smaller cubes.
Total surface area of all small cubes = 1000 × 6 cm² = 6000 cm²
Ratio:
The ratio of the surface area of the larger block to the combined surface area of the smaller cubes is therefore:
600 cm² (larger cube) : 6000 cm² (smaller cubes)
Ratio = 1 : 10