Question 4

We can find the actual geographical distance by multiplying the measured map distance by the map's scale factor.

Step 1 — Understand the Map Scale

The map shows a Representative Fraction (RF) scale. The RF is 1:60,00,000. This means 1 unit on the map represents 60,00,000 units in reality.

Let us convert this scale into a more usable form, like kilometers per centimeter. We know that 1 meter = 100 centimeters and 1 kilometer = 1000 meters.

$1 \text{ cm on map} = 60,00,000 \text{ cm in reality}$

$1 \text{ cm on map} = \frac{60,00,000}{100} \text{ meters in reality}$

$= 60,000 \text{ meters in reality}$

$1 \text{ cm on map} = \frac{60,000}{1000} \text{ kilometers in reality}$

$\boxed{1 \text{ cm on map} = 600 \text{ km in reality}}$

Step 2 — Distance between Bengaluru and Chennai

Let us measure the straight-line distance between Bengaluru and Chennai on the map using a ruler. Let $d_{\text{map1}}$ be this measured distance.

$d_{\text{map1}} = 0.6 \text{ cm}$

Now, we use the scale factor to find the actual geographical distance. Let $D_{\text{actual1}}$ be the actual distance between Bengaluru and Chennai.

$D_{\text{actual1}} = d_{\text{map1}} \times 600 \text{ km/cm}$

$D_{\text{actual1}} = 0.6 \text{ cm} \times 600 \text{ km/cm}$

$= 360 \text{ km}$

$\boxed{\text{Geographical distance between Bengaluru and Chennai} = 360 \text{ km}}$

Step 3 — Distance between Mangaluru and Chennai

Let us measure the straight-line distance between Mangaluru and Chennai on the map using a ruler. Let $d_{\text{map2}}$ be this measured distance.

$d_{\text{map2}} = 1.1 \text{ cm}$

Now, we use the scale factor to find the actual geographical distance. Let $D_{\text{actual2}}$ be the actual distance between Mangaluru and Chennai.

$D_{\text{actual2}} = d_{\text{map2}} \times 600 \text{ km/cm}$

$D_{\text{actual2}} = 1.1 \text{ cm} \times 600 \text{ km/cm}$

$= 660 \text{ km}$

$\boxed{\text{Geographical distance between Mangaluru and Chennai} = 660 \text{ km}}$

Answer

(i) The geographical distance between Bengaluru and Chennai is 360 km. (ii) The geographical distance between Mangaluru and Chennai is 660 km.