On a topographical map drawn to a Representative Fraction (RF) scale of 1 : 100,000, the m… — JAMB UTME

On a topographical map drawn to a Representative Fraction (RF) scale of $1 : 100,000$ , the measured distance between a railway station and a local airstrip is $7.5\text{ cm}$ . What is the actual ground distance between the two locations in kilometers?

Answer: 7.5 km

Answer

The actual ground distance between the railway station and the airstrip is

7.5\text{ km}

Given an RF scale of

1 : 100,000

, every

1\text{ cm}

on the map corresponds to

100,000\text{ cm}

on the ground, which equals

1\text{ km}

. Multiplying the measured map length of

7.5\text{ cm}

1\text{ km}

per centimeter gives an actual ground distance of

7.5\text{ km}

Step-by-Step Solution

Interpret the Representative Fraction (RF) scale.

An RF scale of

1 : 100,000

means

1\text{ cm}

on the map represents

100,000\text{ cm}

on the ground.

RF scale expresses map distance to ground distance in identical units.

Convert the ground distance scale unit from centimeters to kilometers.

100,000\text{ cm} = \frac{100,000}{100,000}\text{ km} = 1\text{ km}

There are

100,000\text{ cm}

1\text{ km}

(

100\text{ cm/m} \times 1,000\text{ m/km}

Calculate the total actual ground distance.

\text{Ground Distance} = 7.5\text{ cm} \times 1\text{ km/cm} = 7.5\text{ km}$.

Multiplying the map length by the real-world distance represented per unit length determines the true distance.

Key Concept

Map Scale Conversion and Ground Distance Calculation

Question

Answer

Step-by-Step Solution

Key Concept

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