A mining concession covers an area of 40\text{ cm}^2 on a topographical map drawn to a sca… — JAMB UTME

A mining concession covers an area of $40\text{ cm}^2$ on a topographical map drawn to a scale of $1 : 50,000$ . If this map is reduced to a scale of $1 : 200,000$ , what is the area of the concession on the reduced map in $\text{cm}^2$ ?

Cevap: 2.5 cm²

Cevap

The area of the mining concession on the reduced map is

2.5\text{ cm}^2

When a map is reduced from a scale of

1 : 50,000

1 : 200,000

, the linear scale is reduced by a factor of

4

(since

200,000 / 50,000 = 4

). Because area changes proportionally to the square of the linear change, the area scale factor is

(1/4)^2 = 1/16

. Multiplying the original area of

40\text{ cm}^2

1/16

gives

2.5\text{ cm}^2

Adım Adım Çözüm

Calculate the linear reduction factor.

Linear scale factor

k = \frac{50,000}{200,000} = \frac{1}{4} = 0.25

The linear change ratio is determined by comparing the old scale denominator to the new scale denominator.

Calculate the area scale factor.

Area factor

k^2 = (0.25)^2 = \frac{1}{16} = 0.0625

Area scale varies with the square of the linear scale factor.

Determine the area on the reduced map.

New Map Area

= 40\text{ cm}^2 \times 0.0625 = 2.5\text{ cm}^2

Applying the area reduction factor to the original map area yields the new map area.

Anahtar Kavram

Relationship between linear scale factor and area scale factor during map reduction

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