A surveyor measures a straight stretch of road between two agricultural settlements on a t… — JAMB UTME

A surveyor measures a straight stretch of road between two agricultural settlements on a topographical map drawn to a scale of $1 : 75,000$ . If the distance between the two settlements on the map is $16\text{ cm}$ , what is the actual ground distance in kilometers?

Cevap: 12 km

Cevap

The actual ground distance between the two settlements is

12\text{ km}

A Representative Fraction scale of

1 : 75,000

means

1\text{ cm}

on the map represents

75,000\text{ cm}

on the ground. Converting

75,000\text{ cm}

into kilometres gives

\frac{75,000}{100,000} = 0.75\text{ km}

. Multiplying the measured map length of

16\text{ cm}

0.75\text{ km/cm}

yields an actual distance of

12\text{ km}

Adım Adım Çözüm

Convert scale denominator from centimetres to kilometres

1\text{ cm on map} = 75,000\text{ cm on ground} = 0.75\text{ km}

Dividing centimetres by

100,000

(

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

) converts centimetres to kilometres.

Calculate the actual ground distance

16\text{ cm} \times 0.75\text{ km/cm} = 12\text{ km}

Multiplying the measured distance on the map by the ground distance represented per centimetre gives the total ground distance.

Anahtar Kavram

Map Scale Conversion and Ground Distance Calculation

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