On a topographical map drawn to a scale of 1 : 40,000, a communications cable line is plan… — JAMB UTME

On a topographical map drawn to a scale of $1 : 40,000$ , a communications cable line is planned between Trigonometrical Station $P$ at an elevation of $680\text{ m}$ and Spot Height $Q$ at an elevation of $200\text{ m}$ . If the straight-line distance measured between $P$ and $Q$ on the map is $12\text{ cm}$ , what is the average gradient of the slope between these two points expressed as a percentage?

$10\%$ Answer
B
$0.1\%$
C
$14.17\%$
D
$4\%$

Answer

The average gradient of the slope expressed as a percentage is

10\%

The slope gradient is calculated by dividing the Vertical Interval (

480\text{ m}

) by the Horizontal Equivalent (

4,800\text{ m}

). Multiplying the ratio

\frac{480}{4,800} = 0.10

100

yields

10\%

Step-by-Step Solution

Calculate the Vertical Interval (VI)

\text{VI} = 680\text{ m} - 200\text{ m} = 480\text{ m}

Vertical Interval is the difference in elevation between the two points.

Calculate the Horizontal Equivalent (HE) in meters

\text{Ground distance} = 12\text{ cm} \times 40,000 = 480,000\text{ cm} = 4,800\text{ m}

Multiply the map distance by the scale factor and convert from centimeters to meters (

100\text{ cm} = 1\text{ m}

Compute the slope gradient as a percentage

\text{Gradient (\%)} = \left( \frac{\text{VI}}{\text{HE}} \right) \times 100 = \left( \frac{480\text{ m}}{4,800\text{ m}} \right) \times 100 = 10\%

Gradient percentage is defined as the ratio of Vertical Interval to Horizontal Equivalent multiplied by 100.

Key Concept

Slope and Gradient Calculation on Topographic Maps

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