On a topographical map drawn to a scale of 1 : 30,000, a straight-line distance of 10\text… — JAMB UTME

On a topographical map drawn to a scale of $1 : 30,000$ , a straight-line distance of $10\text{ cm}$ is measured along a hillside track connecting a radio mast at an elevation of $480\text{ m}$ to a valley bridge at an elevation of $180\text{ m}$ . What is the gradient of the slope between the radio mast and the valley bridge?

$1 \text{ in } 10$ Answer
B
$1 \text{ in } 100$
C
$1 \text{ in } 6.25$
D
$1 \text{ in } 3$

Answer

The gradient of the slope is

1 \text{ in } 10

The slope gradient is defined as the ratio of Vertical Interval (VI) to Horizontal Equivalent (HE). The vertical rise between the radio mast (

480\text{ m}

) and the bridge (

180\text{ m}

) is

300\text{ m}

. The actual ground distance represented by

10\text{ cm}

on a

1 : 30,000

scale map is

10 \times 30,000\text{ cm} = 300,000\text{ cm} = 3,000\text{ m}

. Dividing the vertical rise by the horizontal distance gives

\frac{300}{3000} = \frac{1}{10}

, expressed as a ratio of

1 \text{ in } 10

Step-by-Step Solution

Calculate the Vertical Interval (VI)

\text{VI} = 480\text{ m} - 180\text{ m} = 300\text{ m}

Vertical Interval is the difference in height between the highest point and the lowest point.

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

\text{Ground Distance} = 10\text{ cm} \times 30,000 = 300,000\text{ cm} = 3,000\text{ m}

Multiply map distance by the scale factor and convert from centimeters to meters.

Compute the gradient ratio

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

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

Key Concept

Slope and Gradient Calculation

Estimated Time:1m 30s

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