On a topographical map drawn to a scale of 1 : 50,000, the straight-line distance between … — JAMB UTME

On a topographical map drawn to a scale of $1 : 50,000$ , the straight-line distance between two settlements is measured as $14\text{ cm}$ . What is the actual ground distance between the two settlements in kilometers?

$7.0\text{ km}$ Cevap
B
$3.5\text{ km}$
C
$70.0\text{ km}$
D
$28.0\text{ km}$

Cevap

The actual ground distance between the two settlements is

7.0\text{ km}

The scale

1 : 50,000

means that

1\text{ cm}

on the map represents

50,000\text{ cm}

(or

0.5\text{ km}

) on the ground. Therefore, a distance of

14\text{ cm}

on the map corresponds to

14 \times 0.5\text{ km} = 7.0\text{ km}

on the ground.

Adım Adım Çözüm

Identify the scale ratio and map distance

Map scale

= 1 : 50,000

; Map distance

= 14\text{ cm}

Establishes the given measurements needed for calculation.

Convert the scale denominator from centimeters to kilometers

50,000\text{ cm} = \frac{50,000}{100,000}\text{ km} = 0.5\text{ km}

Since

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

1\text{ cm}

on the map represents

0.5\text{ km}

on the ground.

Calculate the ground distance

Ground distance

= 14\text{ cm} \times 0.5\text{ km/cm} = 7.0\text{ km}

Multiplying map distance by the ground distance per centimeter yields total real-world distance.

Anahtar Kavram

Map Scale and Distance Calculation

Soru

Cevap

Adım Adım Çözüm

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