On a topographical map drawn to a scale of 1 : 25,000, two hilltop stations, Station A and… — JAMB UTME

On a topographical map drawn to a scale of $1 : 25,000$ , two hilltop stations, Station A and Station B, are separated by a map distance of $16\text{ cm}$ . If Station A is situated at an elevation of $580\text{ m}$ above sea level and Station B is at an elevation of $180\text{ m}$ , what is the gradient of the slope between the two stations expressed as the value $N$ in the ratio $1 : N$ ?

Answer: 10

Answer

The denominator

N

in the slope gradient ratio

1 : N

10

(representing a gradient ratio of

1 : 10

To calculate the gradient expressed as

1 : N

, determine the Vertical Interval (VI

= 580\text{ m} - 180\text{ m} = 400\text{ m}

) and the Horizontal Equivalent (HE

= 16\text{ cm} \times 25,000 = 400,000\text{ cm} = 4,000\text{ m}

). Dividing VI by HE gives

\frac{400\text{ m}}{4,000\text{ m}} = \frac{1}{10}

, which corresponds to a gradient of

1 : 10

, making

N = 10

Step-by-Step Solution

Determine the Vertical Interval (VI)

\text{VI} = 580\text{ m} - 180\text{ m} = 400\text{ m}

The Vertical Interval is the vertical height difference between the two specified elevations.

Calculate the Horizontal Equivalent (HE) on the ground

\text{HE} = 16\text{ cm} \times 25,000 = 400,000\text{ cm} = 4,000\text{ m}

Multiply the map distance by the scale denominator to find the ground distance, then divide by 100 to convert centimeters to meters.

Calculate the gradient ratio

\text{Gradient} = \frac{\text{VI}}{\text{HE}} = \frac{400\text{ m}}{4,000\text{ m}} = \frac{1}{10} = 1 : 10

Gradient is calculated as Vertical Interval divided by Horizontal Equivalent, simplified to a fraction with a numerator of 1.

Key Concept

Calculation of slope gradient using vertical interval, map distance, and representative fraction scale

Estimated Time:1m 30s

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