A proposed road route on a topographical map drawn to a scale of 1 : 20,000 connects a riv… — JAMB UTME

A proposed road route on a topographical map drawn to a scale of $1 : 20,000$ connects a river confluence at an elevation of $140\text{ m}$ to a hilltop beacon at an elevation of $340\text{ m}$ . If the distance measured along the route on the map is $8\text{ cm}$ , what is the average gradient of the slope along this route?

$1 \text{ in } 8$ Answer
B
$1 \text{ in } 800$
C
$1 \text{ in } 4.7$
D
$1 \text{ in } 80$

Answer

The average gradient of the slope is

1 \text{ in } 8

The slope gradient is determined by dividing the Vertical Interval by the Horizontal Equivalent. Subtracting the starting height (

140\text{ m}

) from the beacon height (

340\text{ m}

) gives a Vertical Interval of

200\text{ m}

. Converting the

8\text{ cm}

map distance using the scale of

1 : 20,000

yields a Horizontal Equivalent of

1,600\text{ m}

. Dividing

200\text{ m}

1,600\text{ m}

reduces to

\frac{1}{8}

, which gives

1 \text{ in } 8

Step-by-Step Solution

Calculate the Vertical Interval (VI)

\text{VI} = 340\text{ m} - 140\text{ m} = 200\text{ m}

Vertical Interval is the difference in elevation between the highest and lowest points of the slope segment.

Calculate the Horizontal Equivalent (HE) in meters

\text{HE} = 8\text{ cm} \times 20,000 = 160,000\text{ cm} = 1,600\text{ m}

Convert map distance to ground distance using the representative fraction scale (

1\text{ cm}

on map =

20,000\text{ cm} = 200\text{ m}

on ground).

Compute the gradient ratio

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

Gradient is expressed as a ratio of 1 unit vertical rise to

N

units horizontal distance (

1 \text{ in } N

Key Concept

Calculation of slope gradient from topographical map scale and contour elevation values.

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic