Question

In 1:100000 scale map, 1 cm on map corresponds to how many kilometres on the ground?

• A. 1 km
• B. 0.1 km
• C. 10 km
• D. 100 km

Hint:

Useful conversions: \[ \boxed{ \begin{aligned} 1:1000 &\Rightarrow 1\text{ cm}=10\text{ m} 1:10000 &\Rightarrow 1\text{ cm}=100\text{ m} 1:100000 &\Rightarrow 1\text{ cm}=1\text{ km} \end{aligned} } \]

Answer 1

The Correct Option is A

Concept: The representative fraction (RF) of a map is \[ \boxed{\text{RF}=\frac{\text{Map Distance}}{\text{Ground Distance}}} \] For a scale of \[ 1:100000 \] it means \[ 1\text{ cm on map}=100000\text{ cm on ground}. \]

Step 1: Convert ground distance into metres. Since \[ 100\text{ cm}=1\text{ m}, \] \[ 100000\text{ cm} =\frac{100000}{100} =1000\text{ m}. \]

Step 2: Convert metres into kilometres. Since \[ 1000\text{ m}=1\text{ km}, \] therefore \[ 1\text{ cm on map}=1\text{ km on ground}. \] Hence, \[ \boxed{1\text{ cm}=1\text{ km}} \] Therefore, the correct option is \[ \boxed{(A).} \]