A proposed pipeline route between two water reservoirs measures 18\text{ cm} on a regional… — JAMB UTME

A proposed pipeline route between two water reservoirs measures $18\text{ cm}$ on a regional map drawn to a statement scale of $5\text{ cm to } 2\text{ km}$ . If this map is reduced to a Representative Fraction (RF) scale of $1 : 100,000$ , what will be the length of the pipeline route on the reduced map?

$7.2\text{ cm}$ Answer
B
$45.0\text{ cm}$
C
$2.88\text{ cm}$
D
$0.72\text{ cm}$

Answer

7.2\text{ cm}

The original statement scale of

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

means each centimeter on the map corresponds to

0.4\text{ km}

on the ground. An

18\text{ cm}

line therefore represents a total ground distance of

18 \times 0.4\text{ km} = 7.2\text{ km}

. On the new map with an RF scale of

1 : 100,000

1\text{ cm}

represents

100,000\text{ cm}

(or

1\text{ km}

). Converting the

7.2\text{ km}

ground distance onto the new map gives

\frac{7.2\text{ km}}{1\text{ km/cm}} = 7.2\text{ cm}

Step-by-Step Solution

Determine the ground distance represented by

1\text{ cm}

on the original map scale.

Since

5\text{ cm} = 2\text{ km}

1\text{ cm} = \frac{2\text{ km}}{5} = 0.4\text{ km}

(or

40,000\text{ cm}

, giving an RF scale of

1 : 40,000

Converting statement scale to ground distance per centimeter establishes the actual linear distance on Earth.

Calculate the actual ground distance of the pipeline route.

\text{Ground Distance} = 18\text{ cm} \times 0.4\text{ km/cm} = 7.2\text{ km}

(or

720,000\text{ cm}$).

Multiplying the map measurement by the ground equivalence per centimeter yields the true distance.

Calculate the new map length on the reduced map of scale

1 : 100,000

On an RF scale of

1 : 100,000

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

. Therefore, \text{New Map Length} = \frac{7.2\text{ km}}{1\text{ km/cm}} = 7.2\text{ cm}$.

Dividing the true ground distance by the new scale factor gives the updated map distance.

Key Concept

Map scale conversion between statement scale and Representative Fraction (RF), and linear distance scaling.

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