On a regional map (Map X), a straight stretch of a major highway between two towns measure… — JAMB UTME

On a regional map (Map X), a straight stretch of a major highway between two towns measures $15\text{ cm}$ . Map X is drawn to a statement scale of $1\text{ cm to } 2\text{ km}$ . If Map X is reduced to produce Map Y such that Map Y has a Representative Fraction (RF) scale of $1 : 500,000$ , what is the measured length of the same highway on Map Y?

$6.0\text{ cm}$ Cevap
B
$37.5\text{ cm}$
C
$2.4\text{ cm}$
D
$60.0\text{ cm}$

Cevap

The measured length of the highway on Map Y is

6.0\text{ cm}

The ground distance between the two towns is

30\text{ km}

(

15\text{ cm} \times 2\text{ km/cm}

). On Map Y, where

1\text{ cm}

represents

500,000\text{ cm}

(

5\text{ km}

), the measured length is

\frac{30\text{ km}}{5\text{ km/cm}} = 6.0\text{ cm}

Adım Adım Çözüm

Calculate the actual ground distance using Map X.

Ground Distance

= 15\text{ cm} \times 2\text{ km/cm} = 30\text{ km}

Map X's scale of

1\text{ cm to } 2\text{ km}

means each centimeter on the map represents

2\text{ km}

on the ground.

Convert the Representative Fraction (RF) scale of Map Y to a statement scale in kilometers.

Map Y Scale

= 1 : 500,000 \Rightarrow 1\text{ cm to } \frac{500,000}{100,000}\text{ km} = 1\text{ cm to } 5\text{ km}

There are

100,000\text{ cm}

1\text{ km}

, so dividing

500,000

100,000

converts the scale to kilometers.

Calculate the distance on Map Y.

Map Y Distance

= \frac{30\text{ km}}{5\text{ km/cm}} = 6.0\text{ cm}

Dividing the actual ground distance by the ground equivalent per centimeter of Map Y gives the distance on Map Y.

Anahtar Kavram

Map Scale Reduction and Ground Distance Calculation

Tahmini Süre:1m 30s

Soru

Cevap

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