Question

The scale of a map is\[1:20000000\]. On the map, the distance between Cairo and Addis Ababa is 12 cm.
Calculate the distance, in kilometers, between Cairo and Addis Ababa.

Answer 1

Hint:
Here we have to use the concept of scaling to calculate the distance in kilometers between Cairo and Addis Ababa. Scaling is defined as the linear transformation of the objects. So, here first we have to convert the value of the given distance into kilometers. Then we will multiply it with the scaling factor to get the actual value of the distance.

Complete step by step solution:
It is given that the distance between Cairo and Addis Ababa on the map is 12 cm.
Firstly we have to convert the given distance into the kilometers.
We know that \[1km = 1000m\] and \[1m = 100cm\].
So, by dividing the given distance by 100 we will get the distance in meters, and then again by dividing the distance by 1000 we will get the distance into kilometers. Therefore, we get
Distance between Cairo and Addis Ababa on the map in kilometer \[ = \dfrac{{12}}{{100}} \times \dfrac{1}{{1000}} = \dfrac{{12}}{{100000}}\]
Now we have to multiply it with the scaling factor i.e. 20000000 to get the actual distance between Cairo and Addis Ababa.
Therefore, we get
The actual distance between Cairo and Addis Ababa on the map in kilometer \[ = \dfrac{{12}}{{100000}} \times 20000000\]
Simplifying the expression, we get
The actual distance between Cairo and Addis Ababa on the map in kilometer \[ = 12 \times 200 = 2400{\rm{km}}\]

Hence, the distance in kilometers between Cairo and Addis Ababa is 2400 km.

Note:
We have to note that while converting the cm into kilometers we have to divide it with the 100 and 1000 simultaneously rather than multiplying. On the map, scaling is generally used to diminish the whole map so that it can be visible in a compact way because the size of the earth is too large. This is a real-life example of the use of scaling. Scaling is used in a lot of different domains like designing some large objects etc. Scaling can be used to enlarge an object which is too small to be visible like the cells of the human body.