Final answer:
The size-n whole problem involves calculating the actual area represented by a 4 feet by 8 feet N gauge model train display, which, with a scale of 1:160, corresponds to a real-world area of 819,200 square feet.
Step-by-step explanation:
The size-n whole problem in this scenario refers to calculating the real-world area represented by a scaled model in the context of a model train display. Since the scale given is 1:160 (N gauge), and the display area is 4 feet by 8 feet, we must determine what this area size corresponds to in the real world.
First, we find the area of the display in square feet: 4 feet × 8 feet = 32 square feet.
Next, to calculate the real-world area that the display represents, we multiply the display area by the scale factor squared (since scale factors apply to each dimension):
'Real-world area' = 'Display area' × 'Scale factor' × 'Scale factor'
'Real-world area' = 32 sq ft × 160 × 160
'Real-world area' = 32 sq ft × 25600
'Real-world area' = 819200 square feet
Therefore, the display area of 4 feet by 8 feet in N gauge represents an area of 819,200 square feet in the real world.