A wildlife sanctuary covers an area of 24\text{ cm}^2 on Map P, which is drawn to a scale … — JAMB UTME

A wildlife sanctuary covers an area of $24\text{ cm}^2$ on Map P, which is drawn to a scale of $1 : 60,000$ . If Map P is enlarged to produce Map Q with a scale of $1 : 20,000$ , what is the area of the sanctuary on Map Q in $\text{cm}^2$ ?

Cevap: 216 cm²

Cevap

The area of the sanctuary on Map Q is

216\text{ cm}^2

When a map is enlarged from a scale of

1 : 60,000

1 : 20,000

, the linear dimension increases by a factor of

\frac{60,000}{20,000} = 3

. Because area is a two-dimensional measurement, the area scale factor is the square of the linear scale factor (

3^2 = 9

). Thus, the new area on Map Q is

24\text{ cm}^2 \times 9 = 216\text{ cm}^2

Adım Adım Çözüm

Find the linear scale enlargement factor (

k

)

k = \frac{\text{Old Scale Denominator}}{\text{New Scale Denominator}} = \frac{60,000}{20,000} = 3

Enlarging a map scale from

1 : 60,000

1 : 20,000

increases linear dimensions by a factor of 3.

Determine the area scale multiplier

\text{Area Scale Factor} = k^2 = 3^2 = 9

Area changes according to the square of the linear scale change ratio.

Calculate the new map area

24\text{ cm}^2 \times 9 = 216\text{ cm}^2

Multiplying the original area on Map P by the area scale factor yields the enlarged area on Map Q.

Anahtar Kavram

Map Enlargement Area Calculation

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