On a topographical map drawn to a Representative Fraction (RF) scale of 1 : 80,000, the me… — JAMB UTME

On a topographical map drawn to a Representative Fraction (RF) scale of $1 : 80,000$ , the measured distance along a proposed drainage canal between two agricultural communities is $17.5\text{ cm}$ . What is the actual ground distance of the canal in kilometers?

$14.0\text{ km}$ Answer
B
$140.0\text{ km}$
C
$1,400.0\text{ km}$
D
$7.0\text{ km}$

Answer

The actual ground distance of the drainage canal is

14.0\text{ km}

The option showing

14.0\text{ km}

is correct because multiplying the map distance (

17.5\text{ cm}

) by the RF scale factor (

80,000

) gives a ground measurement of

1,400,000\text{ cm}

. Converting to kilometers by dividing by

100,000\text{ cm/km}

yields exactly

14.0\text{ km}

Step-by-Step Solution

Identify the given map scale and distance

Representative Fraction scale =

1 : 80,000

; Map distance =

17.5\text{ cm}

Establishing known values is essential for scale conversion.

Calculate the ground distance in centimeters

Ground distance in cm =

17.5\text{ cm} \times 80,000 = 1,400,000\text{ cm}

The RF denominator indicates that

1\text{ cm}

on the map represents

80,000\text{ cm}

on the ground.

Convert the ground distance from centimeters to kilometers

Ground distance in km =

\frac{1,400,000\text{ cm}}{100,000\text{ cm/km}} = 14.0\text{ km}

Since

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

, dividing by

100,000

converts centimeters to kilometers.

Key Concept

Ground Distance Calculation using Representative Fraction (RF)

Estimated Time:1m 30s

Question

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Step-by-Step Solution

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