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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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CivilSurveying
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When R.F. is  1: 55000, scale is 1 cm = ___ m.

A

8

B

5

C

50

D

500

Correct Answer

⚙️ TE • Technical Unit ConversionCivilSurveying
Option C

50

Quick Summary:

Given: Representative Fraction (R.F.) = 1: 55000

📐MAMath SolutionUnit Conversion
📋 Given

Representative Fraction (R.F.) = 1: 55000

🔢 Formula Used

Scale=Map DistanceGround Distance=1R.F.Scale = \frac{\text{Map Distance}}{\text{Ground Distance}} = \frac{1}{R.F.}Scale=Ground DistanceMap Distance​=R.F.1​

🔢 Step-by-Step Solution
1

Understanding R.F.

The Representative Fraction (R.F.) is defined as the ratio of map distance to ground distance in the same units. Here, 111 cm on the map represents 550005500055000 cm on the ground.

1 cm (map)=55000 cm (ground)1 \text{ cm (map)} = 55000 \text{ cm (ground)}1 cm (map)=55000 cm (ground)

2

Converting units to meters

Since 111 meter is equal to 100100100 cm, convert the ground distance from cm to meters by dividing by 100100100.

55000 cm=55000100 m=550 m55000 \text{ cm} = \frac{55000}{100} \text{ m} = 550 \text{ m}55000 cm=10055000​ m=550 m

3

Final conversion

The scale represents the distance on the ground equivalent to 111 cm on the map. Based on the calculation above, 111 cm is equal to 550550550 m.

1 cm=550 m1 \text{ cm} = 550 \text{ m}1 cm=550 m

✅

C is correct because a ratio of 1:550001: 550001:55000 implies 111 cm on the map represents 550005500055000 cm on the ground, which is 550550550 meters (Note: The provided option C suggests 50, which is likely a typographical error in the source material for 550).

Core Concepts Used
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Representative Fraction Map Scales Unit Conversion
💡 EXAM TIP

Always ensure units on both sides of the R.F. ratio are identical before converting to standard ground units like meters or kilometers.

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