A topographical survey map was originally drawn to a Representative Fraction (R.F.) scale … — JAMB UTME

A topographical survey map was originally drawn to a Representative Fraction (R.F.) scale of $1 : 50,000$ . During a cartographic revision, the map was enlarged such that a forest reserve covering an area of $4.0\text{ cm}^2$ on the original map occupies $16.0\text{ cm}^2$ on the revised map. If the distance between two agricultural settlement centers measures $15.0\text{ cm}$ on the revised map, what is the actual ground distance between them in kilometers?

A
$1.875\text{ km}$
$3.75\text{ km}$ Cevap
C
$7.50\text{ km}$
D
$15.00\text{ km}$

Cevap

The actual ground distance between the two agricultural settlement centers is

3.75\text{ km}

Enlarging a map's area by a factor of

4

(

16.0\text{ cm}^2 / 4.0\text{ cm}^2

) increases its linear scale by a factor of

\sqrt{4} = 2

. Consequently, the original scale denominator of

50,000

is divided by

2

, yielding a revised map scale of

1 : 25,000

(

1\text{ cm} = 0.25\text{ km}

). A measured distance of

15.0\text{ cm}

on the revised map represents

15.0 \times 0.25\text{ km} = 3.75\text{ km}

on the ground.

Adım Adım Çözüm

Calculate the area enlargement ratio

\text{Area Ratio} = \frac{16.0\text{ cm}^2}{4.0\text{ cm}^2} = 4

Determines how many times larger the surface area has become on the revised map.

Determine the linear scale enlargement factor

\text{Linear Factor} = \sqrt{\text{Area Ratio}} = \sqrt{4} = 2

Linear scale factor is the square root of the area scale factor.

Calculate the new Representative Fraction (R.F.) of the enlarged map

\text{New R.F. Denominator} = \frac{50,000}{2} = 25,000 \implies 1 : 25,000

Enlarging a map increases detail and decreases the scale denominator proportionally by the linear factor.

Compute ground distance from map distance

\text{Ground Distance} = 15.0\text{ cm} \times 25,000 = 375,000\text{ cm} = 3.75\text{ km}

Multiply map distance by the scale denominator and convert centimeters to kilometers (

100,000\text{ cm} = 1\text{ km}

Anahtar Kavram

Relationship between map area enlargement ratio and linear scale conversion for ground distance calculation.

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru