On a regional planning map drawn to a Representative Fraction (R.F.) scale of 1 : 80,000, … — JAMB UTME

On a regional planning map drawn to a Representative Fraction (R.F.) scale of $1 : 80,000$ , a proposed bypass road between two industrial hubs measures $16.5\text{ cm}$ . What is the actual ground distance of the bypass road in kilometers?

$13.2\text{ km}$ Answer
B
$132.0\text{ km}$
C
$4.85\text{ km}$
D
$26.4\text{ km}$

Answer

The actual ground distance of the bypass road is

13.2\text{ km}

Multiplying the map distance of

16.5\text{ cm}

by the scale denominator

80,000

yields

1,320,000\text{ cm}

. Converting centimeters to kilometers by dividing by

100,000

correctly yields

13.2\text{ km}

Step-by-Step Solution

Calculate the ground distance in centimeters using the Representative Fraction scale.

\text{Ground Distance (cm)} = 16.5\text{ cm} \times 80,000 = 1,320,000\text{ cm}

The R.F. scale of

1 : 80,000

indicates that

1\text{ cm}

on the map represents

80,000\text{ cm}

on the ground.

Convert the ground distance from centimeters to kilometers.

\text{Ground Distance (km)} = \frac{1,320,000\text{ cm}}{100,000\text{ cm/km}} = 13.2\text{ km}

There are

100,000\text{ cm}

1\text{ km}

(

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

Key Concept

Ground distance calculation from Representative Fraction (R.F.) map scale

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