A proposed industrial estate is represented as a square measuring 6\text{ cm} by 6\text{ c… — JAMB UTME

A proposed industrial estate is represented as a square measuring $6\text{ cm}$ by $6\text{ cm}$ on a topographical map drawn to a scale of $1 : 40,000$ . If the map is reduced to a scale of $1 : 120,000$ , what is the new area of the industrial estate on the reduced map?

$4\text{ cm}^2$ Answer
B
$12\text{ cm}^2$
C
$108\text{ cm}^2$
D
$324\text{ cm}^2$

Answer

The new area of the industrial estate on the reduced map is

4\text{ cm}^2

When a map is reduced from a scale of

1:40,000

1:120,000

, the linear dimensions are reduced by a factor of

\frac{40,000}{120,000} = \frac{1}{3}

. Since area is two-dimensional, the area changes by the square of the linear ratio:

\left(\frac{1}{3}\right)^2 = \frac{1}{9}

. Multiplying the original area of

36\text{ cm}^2

\frac{1}{9}

gives

4\text{ cm}^2

Step-by-Step Solution

Calculate the original area of the feature on the map.

Original area =

6\text{ cm} \times 6\text{ cm} = 36\text{ cm}^2

The feature is rectangular/square, so area on map is length multiplied by width.

Determine the linear scale change ratio.

Linear scale factor =

\frac{\text{Old Scale Denominator}}{\text{New Scale Denominator}} = \frac{40,000}{120,000} = \frac{1}{3}

Changing scale from

1:40,000

1:120,000

reduces all linear dimensions to

1/3

of their original size.

Calculate the area scale factor and final area.

Area scale factor =

\left(\frac{1}{3}\right)^2 = \frac{1}{9}

. New Area =

36\text{ cm}^2 \times \frac{1}{9} = 4\text{ cm}^2

Areal change is proportional to the square of the linear scale ratio.

Key Concept

Relationship between linear scale ratio and area change in map reduction

Estimated Time:1m 30s

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