On a topographical survey map drawn to a scale of 1:40,000, Point X lies at an elevation o… — JAMB UTME

On a topographical survey map drawn to a scale of $1:40,000$ , Point X lies at an elevation of $250\text{ m}$ on a hillside, and Point Y lies further uphill along a straight spur at an elevation of $650\text{ m}$ . If the distance between Point X and Point Y measured on the map is $5\text{ cm}$ , the gradient of the slope between the two points can be expressed in the ratio form $1 : x$ . What is the numerical value of $x$ ?

Cevap: 5

Cevap

The numerical value of

x

is 5.

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

400\text{ m}

. Converting the

5\text{ cm}

map measurement to ground distance using the

1:40,000

scale gives

2,000\text{ m}

(Horizontal Equivalent). Dividing the Vertical Interval by the Horizontal Equivalent yields

\frac{400}{2000} = \frac{1}{5}

, meaning the gradient expressed as

1 : x

has

x = 5

Adım Adım Çözüm

Calculate the Vertical Interval (VI)

400 m

The vertical interval represents the elevation difference between Point Y and Point X:

650\text{ m} - 250\text{ m} = 400\text{ m}

Calculate the Horizontal Equivalent (HE)

2,000 m

At a map scale of

1:40,000

1\text{ cm}

on the map corresponds to

40,000\text{ cm} = 400\text{ m}

on the ground. A map measurement of

5\text{ cm}

equals

5 \times 400\text{ m} = 2,000\text{ m}

Determine the Gradient Ratio

1 : 5 (x = 5)

Gradient is determined by dividing Vertical Interval by Horizontal Equivalent:

\frac{400\text{ m}}{2,000\text{ m}} = \frac{1}{5}

. Writing this ratio as

1 : x

yields

x = 5

Anahtar Kavram

Slope and Gradient Calculation from Topographical Contour Maps

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