Final answer:
To determine the area of copper foil covering the steeple, the side length of the hexagonal base is calculated using the lateral area of the tower, then the area of one triangle is found and multiplied by six. The total copper foil covering the steeple amounts to 24√3 m², which corresponds to option B.
Step-by-step explanation:
To find the exact amount of copper foil covering the steeple, which is a pyramid with a regular hexagonal base composed of equilateral triangles, we need to calculate the surface area of one of the triangles and then multiply by 6 since a hexagon has 6 sides.
Since the pyramid and the tower have the same hexagonal base, we can calculate the side length of the hexagon using the lateral area of the tower, which is given to be 2400 m². The lateral area of a prism is the perimeter of the base times the height of the prism. For a hexagon, this perimeter (P) is 6 times the side length (s). Therefore, P = 6s.
We can set up the equation for the lateral area of the tower (L) as 6s × height = 2400 m². Since the height given is 100 m, we can solve for the side length (s):
L = 6s × 100 m = 2400 m² \Rightarrow s = × 2400 m² / 600 m = 4 m
Now, we know the side length of an equilateral triangle that forms each face of the pyramid base is 4 m. The area (A) of an equilateral triangle with side length (s) is given by the formula A = (√3 / 4)s². Plugging in our side length, A = (√3 / 4)(4 m)² = 4√3 m².
Finally, to find the total area covered by copper foil on the steeple, we multiply the area of one triangle by the number of triangles (6): Total area = 6 × 4√3 m² = 24√3 m².