A county boundary encloses an area of 72\text{ cm}^2 on Map A, which is drawn at a scale o… — JAMB UTME

A county boundary encloses an area of $72\text{ cm}^2$ on Map A, which is drawn at a scale of $1 : 20,000$ . Map A is reduced to produce Map B, which has a Representative Fraction of $1 : 60,000$ . What is the area of the county boundary on Map B?

$8\text{ cm}^2$ Answer
B
$24\text{ cm}^2$
C
$216\text{ cm}^2$
D
$648\text{ cm}^2$

Answer

The area of the county boundary on Map B is

8\text{ cm}^2

The linear reduction ratio from a scale of

1 : 20,000

1 : 60,000

\frac{20,000}{60,000} = \frac{1}{3}

. Because area is a two-dimensional quantity, the area scale factor is the square of the linear factor, which is

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

. Applying this area scale factor to the original map area of

72\text{ cm}^2

gives

72\text{ cm}^2 \times \frac{1}{9} = 8\text{ cm}^2

Step-by-Step Solution

Determine the linear scale reduction factor (

k

) between Map A and Map B.

k = \frac{\text{Scale Denominator of Map A}}{\text{Scale Denominator of Map B}} = \frac{20,000}{60,000} = \frac{1}{3}

Map scale reduction decreases linear dimensions proportionally to the ratio of the original scale denominator to the new scale denominator.

Calculate the area scale change factor (

k^2

\text{Area Scale Factor} = k^2 = \left(\frac{1}{3}\right)^2 = \frac{1}{9}

Surface area changes according to the square of the linear scale factor.

Calculate the new area on Map B using the original map area.

\text{New Area} = 72\text{ cm}^2 \times \frac{1}{9} = 8\text{ cm}^2

Multiplying the initial map area by the area scale change factor yields the reduced map area.

Key Concept

Relationship between linear scale change and area scale change in map reduction

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic