A forest reserve covers an area of 16\text{ cm}^2 on a topographical map with a scale of 1… — JAMB UTME

A forest reserve covers an area of $16\text{ cm}^2$ on a topographical map with a scale of $1 : 100,000$ . If the map is enlarged such that the same forest reserve occupies an area of $64\text{ cm}^2$ on the new map, what is the scale denominator ( $N$ ) of the new map, where the scale is expressed as $1 : N$ ?

Answer: 50000

Answer

The scale denominator of the new map is 50,000.

To find the scale denominator of the enlarged map, first determine the area multiplier by dividing the new map area by the original map area (

64\text{ cm}^2 / 16\text{ cm}^2 = 4

). Since map area scale is the square of the linear scale multiplier (

k^2 = 4

), taking the square root gives the linear factor

k = 2

. Map enlargement by a linear factor of

2

means the map detail is twice as large, so the new scale denominator is found by dividing the original denominator by

2

100,000 / 2 = 50,000

. The scale of the new map is

1 : 50,000

Step-by-Step Solution

Calculate the area scale multiplier

Area multiplier = 64 / 16 = 4

The area scale multiplier is the ratio of the new feature area on the map to its original area on the map.

Calculate the linear scale multiplier

Linear multiplier = sqrt(4) = 2

Map area varies as the square of the linear scale multiplier (k^2), so the linear multiplier k is the square root of the area multiplier.

Calculate the new scale denominator

New scale denominator N = 100,000 / 2 = 50,000

When a map is enlarged by a linear factor k, its representative fraction denominator is divided by k.

Key Concept

Map Enlargement and Area Scale Calculations

Estimated Time:1m 30s

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