During a mapwork exercise on a topographical map with a scale of 1 : 100,000, a student id… — JAMB UTME

During a mapwork exercise on a topographical map with a scale of $1 : 100,000$ , a student identifies a river bed at an elevation of $120\text{ m}$ and a hilltop trigonometric station at an elevation of $320\text{ m}$ . If the map distance between these two points is $4\text{ cm}$ , what is the average gradient of the slope?

$1 \text{ in } 20$ Answer
B
$1 \text{ in } 50$
C
$1 \text{ in } 12.5$
D
$1 \text{ in } 2$

Answer

The average gradient of the slope is

1 \text{ in } 20

The slope gradient is calculated by taking the ratio of Vertical Interval (VI) to Horizontal Equivalent (HE). The vertical rise between the river bed and the trigonometric station is

320\text{ m} - 120\text{ m} = 200\text{ m}

. Using the map scale of

1 : 100,000

, a map distance of

4\text{ cm}

corresponds to

400,000\text{ cm}

4,000\text{ m}

on ground. Dividing

200\text{ m}

4,000\text{ m}

yields

\frac{1}{20}

, which is expressed as

1 \text{ in } 20

Step-by-Step Solution

Calculate the Vertical Interval (VI)

\text{VI} = 320\text{ m} - 120\text{ m} = 200\text{ m}

Vertical interval is the difference in height between the higher point and the lower point.

Calculate the Horizontal Equivalent (HE) in real-world meters using the map scale

\text{HE} = 4\text{ cm} \times 100,000 = 400,000\text{ cm} = 4,000\text{ m}

To find actual ground distance, multiply the map distance by the scale denominator and convert centimeters to meters.

Compute the gradient ratio

\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{200\text{ m}}{4,000\text{ m}} = \frac{1}{20} = 1 \text{ in } 20

Gradient is expressed as a ratio of vertical rise to horizontal distance.

Key Concept

Calculation of slope gradient from topographic map elevation points and representative fraction scale

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