On a topographical map with a scale of 1 : 50,000, two hilltops are located at elevations … — JAMB UTME

On a topographical map with a scale of $1 : 50,000$ , two hilltops are located at elevations of $750\text{ m}$ and $450\text{ m}$ respectively. If the straight-line distance separating the two hilltops on the map is $6\text{ cm}$ , what is the average gradient between them?

$1\text{ in }10$ Answer
B
$1\text{ in }50$
C
$1\text{ in }100$
D
$1\text{ in }4$

Answer

The average gradient between the two hilltops is

1\text{ in }10

The vertical interval (VI) is the difference in elevation:

750\text{ m} - 450\text{ m} = 300\text{ m}

. The horizontal equivalent (HE) is the ground distance:

6\text{ cm} \times 50,000 = 300,000\text{ cm} = 3,000\text{ m}

. The gradient is

\frac{\text{VI}}{\text{HE}} = \frac{300}{3,000} = \frac{1}{10}

, expressed as

1\text{ in }10

Step-by-Step Solution

Calculate the Vertical Interval (VI)

\text{VI} = 750\text{ m} - 450\text{ m} = 300\text{ m}

Gradient requires the difference in elevation between the two specified points.

Calculate the Horizontal Equivalent (HE) on the ground in meters

\text{HE} = 6\text{ cm} \times 50,000 = 300,000\text{ cm} = 3,000\text{ m}

Map distance must be converted to actual ground distance using the representative fraction scale.

Calculate the gradient using the formula

\text{Gradient} = \frac{\text{VI}}{\text{HE}}

\text{Gradient} = \frac{300\text{ m}}{3,000\text{ m}} = \frac{1}{10}

1\text{ in }10

Dividing the vertical interval by the horizontal equivalent in identical units yields the ratio slope.

Key Concept

Topographic gradient calculation from map scale and elevation differences

Estimated Time:1m 30s

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