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?

Answer: 12 km

Answer

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}

Step-by-Step Solution

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.

Key Concept

Map Scale Conversion and Ground Distance Calculation

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic