To find the actual distance from town A to town B, given the scale of [tex]\(1 \text{ cm} : 100 \text{ km}\)[/tex], we need to follow these steps:
1. Identify the scale: The scale provided is [tex]\(1 \text{ cm}\)[/tex] on the map represents [tex]\(100 \text{ km}\)[/tex] in reality.
2. Determine the distance on the map: The distance between town A and town B on the map is given as 400 cm.
3. Calculate the actual distance:
- Since [tex]\(1 \text{ cm}\)[/tex] represents [tex]\(100 \text{ km}\)[/tex],
- We can multiply the distance on the map by the scale factor to find the actual distance.
- The scale factor here is 100 km/cm.
4. Perform the multiplication:
[tex]\[
\text{Actual distance} = 400 \text{ cm} \times 100 \text{ km/cm}
\][/tex]
5. Result:
[tex]\[
\text{Actual distance} = 40000 \text{ km}
\][/tex]
Therefore, the actual distance from town A to town B is [tex]\(\boxed{40000 \text{ km}}\)[/tex], which corresponds to option A.
