A forest reserve is represented as a rectangular feature measuring 8\text{ cm} by 10\text{… — JAMB UTME

A forest reserve is represented as a rectangular feature measuring $8\text{ cm}$ by $10\text{ cm}$ on Map X, which is drawn to a scale of $1 : 50,000$ . On a newly drawn map, Map Y, the same forest reserve occupies an area of $320\text{ cm}^2$ . What is the representative fraction scale of Map Y?

$1 : 25,000$ Cevap
B
$1 : 12,500$
C
$1 : 100,000$
D
$1 : 200,000$

Cevap

The representative fraction scale of Map Y is

1 : 25,000

The original map area is

80\text{ cm}^2

and the enlarged area on Map Y is

320\text{ cm}^2

, giving an area scale factor of

4

. Taking the square root gives a linear scale factor of

2

. Dividing the original scale denominator of

50,000

2

gives

25,000

, resulting in a scale of

1 : 25,000

Adım Adım Çözüm

Calculate the area of the forest reserve on Map X

\text{Area on Map X} = 8\text{ cm} \times 10\text{ cm} = 80\text{ cm}^2

Finding the initial area on the original map is required to determine the area enlargement ratio.

Calculate the area scale factor between Map X and Map Y

\text{Area Scale Factor} = \frac{\text{Area on Map Y}}{\text{Area on Map X}} = \frac{320\text{ cm}^2}{80\text{ cm}^2} = 4

The area scale factor indicates how many times larger the surface area appears on Map Y compared to Map X.

Determine the linear scale factor

\text{Linear Scale Factor} = \sqrt{\text{Area Scale Factor}} = \sqrt{4} = 2

Because surface area changes as the square of linear dimensions (

n^2

), the linear scale factor

n

is the square root of the area factor.

Calculate the new representative fraction scale for Map Y

\text{New Scale Denominator} = \frac{50,000}{2} = 25,000 \Rightarrow 1 : 25,000

Map enlargement increases the scale of the map, which means decreasing the scale denominator by dividing it by the linear scale factor.

Anahtar Kavram

Linear vs. Area Scale Relationship in Map Enlargement

Tahmini Süre:1m 30s

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