On a topographical map with a scale of 1 : 20,000, a proposed electric transmission line e… — JAMB UTME

On a topographical map with a scale of $1 : 20,000$ , a proposed electric transmission line extends from Point $K$ situated on a ridge contour of $650\text{ m}$ to Point $L$ located near a stream contour of $450\text{ m}$ . If the measured distance between Point $K$ and Point $L$ on the map is $8.0\text{ cm}$ , what is the gradient of the slope between these two points?

$1 \text{ in } 8$ Answer
B
$1 \text{ in } 4$
C
$1 \text{ in } 12.5$
D
$1 \text{ in } 125$

Answer

The gradient between Point

K

and Point

L

1 \text{ in } 8

The slope gradient is calculated using the formula

\text{Gradient} = \frac{\text{Vertical Interval}}{\text{Horizontal Equivalent}}

. The Vertical Interval is

650\text{ m} - 450\text{ m} = 200\text{ m}

. The Horizontal Equivalent is calculated by multiplying the map measurement (

8.0\text{ cm}

) by the representative fraction scale factor (

20,000

), yielding

160,000\text{ cm}

, which converts to

1,600\text{ m}

. Placing these in the gradient ratio yields

\frac{200}{1,600} = \frac{1}{8}

, expressed as

1 \text{ in } 8

Step-by-Step Solution

Calculate the Vertical Interval (VI)

\text{VI} = 650\text{ m} - 450\text{ m} = 200\text{ m}

The Vertical Interval is the difference in elevation between the highest and lowest contour points.

Calculate the Horizontal Equivalent (HE) in ground units

\text{HE} = 8.0\text{ cm} \times 20,000 = 160,000\text{ cm} = 1,600\text{ m}

Map distance must be multiplied by the scale factor and converted into meters to match the Vertical Interval unit.

Compute the slope gradient ratio

\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{200\text{ m}}{1,600\text{ m}} = \frac{1}{8}

Gradient is expressed as the ratio of Vertical Interval to Horizontal Equivalent.

Key Concept

Slope and Gradient Calculation from Topographic Maps

Estimated Time:2m 0s

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