A wildlife sanctuary occupies an area of 48\text{ cm}^2 on a topographical map drawn at a … — JAMB UTME

A wildlife sanctuary occupies an area of $48\text{ cm}^2$ on a topographical map drawn at a scale of $1 : 100,000$ . If the map is reduced to a new scale of $1 : 400,000$ , what is the area of the sanctuary on the new map in $\text{cm}^2$ ?

Answer: 3 cm²

Answer

The area of the sanctuary on the reduced map is

3\text{ cm}^2

When a map scale is reduced from

1 : 100,000

1 : 400,000

, the linear dimension reduces by a factor of

4

(since

\frac{100,000}{400,000} = \frac{1}{4}

). Because area is two-dimensional, the area changes by the square of the linear reduction factor, which is

\left(\frac{1}{4}\right)^2 = \frac{1}{16}

. Therefore, the area on the new map is

48\text{ cm}^2 \times \frac{1}{16} = 3\text{ cm}^2

Step-by-Step Solution

Determine the linear scale factor between the original and new scales

Linear scale factor =

\frac{\text{Original Scale Denominator}}{\text{New Scale Denominator}} = \frac{100,000}{400,000} = \frac{1}{4}

When a map scale changes from

1 : 100,000

1 : 400,000

, every linear dimension on the map is reduced to

\frac{1}{4}

of its original length.

Calculate the area reduction factor

Area scale factor =

\left(\frac{1}{4}\right)^2 = \frac{1}{16}

Map area scales as the square of the linear scale factor (

n^2

Calculate the new area on the reduced map

New Area =

48\text{ cm}^2 \times \frac{1}{16} = 3\text{ cm}^2

Multiplying the original area by the area scale factor gives the area representation on the new map.

Key Concept

Map Reduction and Area Scale Factor Relationship

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic