On a topographical map representing a mountainous terrain, a lower index contour line is m… — JAMB UTME

On a topographical map representing a mountainous terrain, a lower index contour line is marked at $500\text{ m}$ above sea level and a higher index contour line is marked at $900\text{ m}$ above sea level. If there are $4$ equal contour intervals between these two index contours, what is the elevation in metres of the third contour line above the $500\text{ m}$ index contour?

Answer: 800 m

Answer

The elevation of the third contour line above the

500\text{ m}

index contour is

800\text{ m}

The vertical difference between the

500\text{ m}

and

900\text{ m}

index contours is

400\text{ m}

. Dividing this difference by the

4

contour intervals gives a uniform vertical interval of

100\text{ m}

per contour line. Therefore, three contour lines above the

500\text{ m}

line correspond to an elevation of

500\text{ m} + 3(100\text{ m}) = 800\text{ m}

Step-by-Step Solution

Find the total elevation difference between the two known index contours

900\text{ m} - 500\text{ m} = 400\text{ m}

This establishes the cumulative elevation change across the four intervals.

Calculate the Vertical Interval (V.I.) between adjacent contour lines

\frac{400\text{ m}}{4} = 100\text{ m}

The contour interval is uniform across the map, so dividing the vertical change by the number of spaces yields the elevation change per line.

Calculate the elevation at the third contour line above the base index contour

500\text{ m} + (3 \times 100\text{ m}) = 800\text{ m}

Moving up three contour lines from

500\text{ m}

increases the elevation by three times the vertical interval.

Key Concept

Vertical Interval and Contour Line Elevation Determination

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