Map Area Calculation Using Scale
The problem requires calculating the area on a map corresponding to a real-world area, given a linear scale.
Understanding the Scale Factor
The given scale is 0.05 cm : 1 km. This means 0.05 centimetres on the map represents 1 kilometre in reality.
Converting Linear Scale to Area Scale
Area is a two-dimensional measurement. To find the area scale, we square the linear scale factor.
- Linear Scale: $0.05\ cm / 1\ km$
- Area Scale: $(0.05\ cm / 1\ km)^2 = (0.05)^2\ cm^2 / (1)^2\ km^2$
- Area Scale: $0.0025\ cm^2 / 1\ km^2$
This means $0.0025$ square centimetres on the map represents 1 square kilometre in reality.
Calculating the Map Area
The actual area of the country is given as $8000\ km^2$. To find the corresponding area on the map, multiply the actual area by the area scale factor.
- Map Area = Actual Area $\times$ Area Scale
- Map Area = $8000\ km^2 \times (0.0025\ cm^2 / 1\ km^2)$
- Map Area = $8000 \times 0.0025\ cm^2$
- Map Area = $20\ cm^2$
Final Answer
The area represented on the map is $20\ cm^2$. This corresponds to Option B.
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Important Questions from Ratio and Proportion
In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
