Final answer:
To find the distance around the edge of the building, we need to find the perimeter of the two cube-shaped pieces. The larger cube has a perimeter of 480 m and the smaller cube has a perimeter of 192 m. The total distance is 672 m.
Step-by-step explanation:
To find the distance around the edge of the building, we need to find the perimeter of the two cube-shaped pieces. The larger part has a volume of 65,000 m³ and the smaller part has a volume of 4000 m³. Since volume of a cube is equal to (side length)^3, we can find the side lengths of both cubes by taking the cube root of their volumes. The larger cube has a side length of ∛(65000) = 40 m and the smaller cube has a side length of ∛(4000) = 16 m.
The formula to find the perimeter of a cube is P = 12s, where P is the perimeter and s is the side length of the cube. For the larger cube, the perimeter is 12 * 40 = 480 m. For the smaller cube, the perimeter is 12 * 16 = 192 m. The total distance around the edge of the building is the sum of the perimeters of the two cubes, so the final answer is 480 m + 192 m = 672 m.