A topographic cross-section is constructed from a map with a horizontal scale of 1 : 50{}0… — JAMB UTME

A topographic cross-section is constructed from a map with a horizontal scale of $1 : 50{}000$ . If the vertical scale of the cross-section is set at $1\text{ cm}$ to represent $100\text{ m}$ , what is the vertical exaggeration of the cross-section?

Answer: 5

Answer

The vertical exaggeration of the cross-section is 5.

To find vertical exaggeration, both scales must be in representative fraction (R.F.) form. A vertical scale of

1\text{ cm}

100\text{ m}

equals

1 : 10{}000

. Dividing the horizontal scale denominator (

50{}000

) by the vertical scale denominator (

10{}000

) gives a vertical exaggeration of

5

Step-by-Step Solution

Convert the vertical scale to a representative fraction

Vertical Scale = 1 : 10,000

Units must be consistent (centimetres to centimetres) to obtain a non-dimensional ratio.

Divide the horizontal scale denominator by the vertical scale denominator

50,000 / 10,000 = 5

Vertical exaggeration measures how many times greater the vertical scale is than the horizontal scale.

Key Concept

Vertical Exaggeration of Cross-Sections

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