On a topographical map of a river basin drawn to a Representative Fraction (R.F.) scale of… — JAMB UTME

On a topographical map of a river basin drawn to a Representative Fraction (R.F.) scale of $1 : 40,000$ , the distance along a proposed drainage channel between two agricultural settlements measures $14.5\text{ cm}$ . What is the actual ground distance of the drainage channel in kilometers?

Answer: 5.8 km

Answer

The actual ground distance of the drainage channel is

5.8\text{ km}

The correct answer of

5.8\text{ km}

is obtained by multiplying the map distance of

14.5\text{ cm}

by the R.F. denominator

40,000

(

14.5 \times 40,000 = 580,000\text{ cm}

) and then converting centimeters to kilometers by dividing by

100,000

(

580,000 \div 100,000 = 5.8\text{ km}

Step-by-Step Solution

Calculate the total ground distance in centimeters

580,000\text{ cm}

According to the R.F. scale of

1 : 40,000

1\text{ cm}

on the map represents

40,000\text{ cm}

on the ground.

Convert the ground distance from centimeters to kilometers

5.8\text{ km}

Since

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

, divide the total distance in centimeters by

100,000

Key Concept

Ground distance calculation using Representative Fraction (R.F.) scale

Estimated Time:1m 15s

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