On a topographical map drawn to a scale of 1 : 40,000, the measured length of a railway li… — JAMB UTME

On a topographical map drawn to a scale of $1 : 40,000$ , the measured length of a railway line is $17.5\text{ cm}$ . If the map is enlarged so that a statement scale of $1\text{ cm to } 250\text{ m}$ applies, what is the length of the railway line on the new enlarged map, in centimeters?

Answer: 28 cm

Answer

The length of the railway line on the enlarged map is

28\text{ cm}

To find the distance on the enlarged map, first calculate the actual ground distance by multiplying the original map distance (

17.5\text{ cm}

) by the scale denominator (

40,000

), yielding

700,000\text{ cm}

7,000\text{ m}

. Next, divide this ground distance by the ground distance represented per centimeter on the new map (

250\text{ m}

), which yields

28\text{ cm}

Step-by-Step Solution

Calculate the actual ground distance using the original map scale and measured distance.

Ground distance =

17.5\text{ cm} \times 40,000 = 700,000\text{ cm} = 7,000\text{ m}

Multiplying the map distance by the scale factor gives the true ground distance.

Calculate the corresponding distance on the enlarged map using the new statement scale.

New map distance =

\frac{7,000\text{ m}}{250\text{ m/cm}} = 28\text{ cm}

Dividing the total ground distance by the ground distance represented per centimeter on the new map yields the map measurement.

Key Concept

Ground distance calculation and map scale conversion during map enlargement.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic