A forest reserve covers an area of 18\text{ cm}^2 on a topographical map drawn to a scale … — JAMB UTME

A forest reserve covers an area of $18\text{ cm}^2$ on a topographical map drawn to a scale of $1 : 150,000$ . If the map is enlarged so that a statement scale of $1\text{ cm}$ to $0.5\text{ km}$ is used for the new map, what is the area of the forest reserve on the enlarged map in $\text{cm}^2$ ?

Cevap: 162 cm²

Cevap

The area of the forest reserve on the enlarged map is

162\text{ cm}^2

The original scale

1 : 150,000

is enlarged to

1 : 50,000

(

1\text{ cm}

0.5\text{ km}

), giving a linear enlargement factor of

n = 150,000 / 50,000 = 3

. Since area changes by the square of the linear scale multiplier (

n^2 = 3^2 = 9

), the new area on the map is

18\text{ cm}^2 \times 9 = 162\text{ cm}^2

Adım Adım Çözüm

Convert the new statement scale to a Representative Fraction (R.F.)

New scale R.F. is

1 : 50,000

Both scales must be in the same format to compare denominators directly (

0.5\text{ km} = 50,000\text{ cm}

Calculate the linear enlargement factor (

n

)

n = \frac{150,000}{50,000} = 3

The linear enlargement factor is found by dividing the original scale denominator by the new scale denominator.

Calculate the area enlargement factor (

n^2

)

Area enlargement factor

= 3^2 = 9

Area changes by the square of the linear scale factor.

Calculate the area on the enlarged map

18\text{ cm}^2 \times 9 = 162\text{ cm}^2

Multiplying the original area on the map by the area enlargement factor yields the new map area.

Anahtar Kavram

Relationship between linear scale factor and area scale factor in map enlargement

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