A proposed rural electrification line connecting a community to a regional substation meas… — JAMB UTME

A proposed rural electrification line connecting a community to a regional substation measures $15.6\text{ cm}$ on a topographical map drawn to a Representative Fraction (R.F.) scale of $1 : 50,000$ . What is the actual length of the power line on the ground in kilometers?

A
$3.12\text{ km}$
$7.8\text{ km}$ Answer
C
$15.6\text{ km}$
D
$78.0\text{ km}$

Answer

7.8\text{ km}

The Representative Fraction scale of

1 : 50,000

indicates that

1\text{ cm}

on the map represents

50,000\text{ cm}

(

0.5\text{ km}

) on the ground. Multiplying the map distance of

15.6\text{ cm}

0.5\text{ km/cm}

gives the actual ground distance of

7.8\text{ km}

Step-by-Step Solution

Calculate total ground distance in centimeters using the R.F. scale

15.6\text{ cm} \times 50,000 = 780,000\text{ cm}

An R.F. scale of

1 : 50,000

means

1\text{ unit}

on the map equals

50,000\text{ units}

on the ground.

Convert centimeters to kilometers

\frac{780,000\text{ cm}}{100,000\text{ cm/km}} = 7.8\text{ km}

There are

100,000\text{ centimeters}

1\text{ kilometer}

Key Concept

Map Scale Distance Calculation

Estimated Time:1m 30s

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