On a topographical map drawn to a scale of 1 : 25,000, a road ascends continuously from Po… — JAMB UTME

On a topographical map drawn to a scale of $1 : 25,000$ , a road ascends continuously from Point X at an elevation of $120\text{ m}$ to Point Y at an elevation of $370\text{ m}$ . If the average gradient of the slope along this road is $1 \text{ in } 20$ , what is the distance between Point X and Point Y on the map?

$20\text{ cm}$ Answer
B
$0.2\text{ cm}$
C
$5\text{ cm}$
D
$29.6\text{ cm}$

Answer

The distance between Point X and Point Y on the map is

20\text{ cm}

The elevation difference (Vertical Interval) between the two points is

370\text{ m} - 120\text{ m} = 250\text{ m}

. Given a gradient of

1 \text{ in } 20

, the horizontal distance on the ground is

250\text{ m} \times 20 = 5,000\text{ m}

(

500,000\text{ cm}

). Dividing this by the scale factor of

25,000

yields a map distance of

20\text{ cm}

Step-by-Step Solution

Calculate the Vertical Interval (VI)

\text{VI} = 370\text{ m} - 120\text{ m} = 250\text{ m}

Vertical interval is the difference in height between the two contour points.

Calculate the Horizontal Equivalent (HE) on the ground using the gradient formula

\text{HE} = \text{VI} \times 20 = 250\text{ m} \times 20 = 5,000\text{ m}

Gradient is given as

\text{VI} / \text{HE} = 1 / 20

, so

\text{HE} = 20 \times \text{VI}

Convert the ground distance to centimeters and calculate the map distance using the scale

1 : 25,000

\text{Ground distance} = 5,000\text{ m} = 500,000\text{ cm}

;

\text{Map distance} = \frac{500,000\text{ cm}}{25,000} = 20\text{ cm}

To find distance on the map, convert the ground measurement to centimeters and divide by the scale denominator.

Key Concept

Topographical Gradient and Scale Conversion

Estimated Time:1m 30s

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