K2KARAKORAM
मराठीEnglish
Open the app

State Board · Class 8 · Geography

Lesson 9: Map Scale

5 concepts · 40 practice questions with answers · Free to read

This lesson is also in: मराठी

Need for map scale and the idea of ratio

From daily life

A passport photo shows you much smaller than you are, but your friends still look in proportion. Every part of you was reduced by the same amount. A map does this to the ground.

Simple definition

Map scale (नकाशा प्रमाण) is the ratio of the map distance to the ground distance.

Rule 1: Photograph and ratio — In a photograph everyone's height shrinks in the same proportion. Example: a boy is 120 cm tall but 8 cm in the photo → ratio 8:120 = 1:15. Map scale uses the same idea. Using it, large ground distances are drawn on paper with Mathematics and Geometry. A painter, too, first fixes the scale of the scene.

6 cm21 cmPhotographReal heightof the boy:120 cm

In the figure : In the figure in a photograph every height is reduced in the same ratio (here 6 cm for a real 120 cm, that is 1:20); map scale uses the same idea (sample values).

  • Easy : Easy: 6 cm for 120 cm is 1:20.
  • Medium : Medium: At 1:20 a 200 cm door is 200 ÷ 20 = 10 cm.
  • Exam-type : Exam: Why do all heights shrink equally?

Rule 2: Scale on every map — The scale must be written on every map; it helps us read the map and understand ground distances. Example: with 1 cm = 5 km, villages 35 km apart are 35 ÷ 5 = 7 cm apart on the map.

PXYno scale givenQXY3.5 cmScale: 1 cm = 4 km

In the figure : In the figure scale must be mentioned on every map: with 1 cm = 4 km, a line of 3.5 cm stands for 14 km (sample values).

  • Easy : Easy: 1 cm = 4 km.
  • Medium : Medium: 3.5 × 4 = 14 km.
  • Exam-type : Exam: Why is scale shown on a map?
Remember

Scale = map distance : ground distance. Every map needs it.

Common mistake

Thinking scale is only for big maps. Every map has one.

Shortcut

Memory clue: "नकाशा : जमीन" म्हणजे प्रमाण.

Spot the difference

ItemMeaning
Map distanceDistance on paper
Ground distanceReal distance
ScaleRatio of the two

Practice questions

Easy
  1. 1What is map scale?
  2. 2Why is it needed on a map?
  3. 3A boy is 120 cm and 8 cm in a photo. Find the ratio.
Medium
  1. 41 cm = 10 km. Map distance 4 cm. Ground?
  2. 51 cm = 5 km. Ground 35 km. Map distance?
  3. 6Does a photo reduce all heights equally?
Challenging
  1. 71 cm = 20 km. Two towns are 3.5 cm apart. Real distance?
  2. 8Why can't we draw a district map at real size?
Show answers (try them yourself first)
  1. 1Ratio of map distance to ground distance.
  2. 2To read ground distances.
  3. 38:120 = 1:15.
  4. 440 km.
  5. 57 cm.
  6. 6Yes, in the same ratio.
  7. 73.5 × 20 = 70 km.
  8. 8It would be too large for paper.

Verbal, numerical and linear (graphical) scales

From daily life

The same speed can be told as "60 km per hour", "1 km per minute" or marked on the speedometer dial. Likewise one map scale can be told in three ways.

Simple definition

The three ways are the verbal scale (शाब्दिक), the numerical scale (संख्यात्मक, RF) and the linear or graphical scale (रेषीय).

Rule 1: Three kinds of scale — Verbal: in words, e.g. 1 cm = 60 km. Numerical (Representative Fraction, RF): a ratio, e.g. 1:60,00,000; 1 is map distance, 60,00,000 ground distance; same unit on both sides, so it is a global scale. Linear: a line divided into units, e.g. 0, 60, 120, 180 km. On a scale, the left side is the map and the right side is the ground.

Verbal1 cm = 40 kmNumerical1:40,00,000Linear04080km

In the figure : In the figure the same scale can be shown in three ways: a verbal scale (in words), a numerical scale (a ratio, RF) and a linear (graphical) scale (a line divided into units).

  • Easy : Easy: There are 3 kinds.
  • Medium : Medium: RF has no units.
  • Exam-type : Exam: Why is RF called global?

Rule 2: Reading the linear scale — Place the distance between two points against the line scale and read it. If a ruler is not available, use a compass, a blade of grass, or a thread for curves.

XY04080120kmschematic strip of a map

In the figure : In the figure the distance between two points is read from the linear scale: here Y is midway between 80 and 120, so X to Y is 100 km (sample values).

  • Easy : Easy: Y is midway, so 100 km.
  • Medium : Medium: (80 + 120) ÷ 2 = 100.
  • Exam-type : Exam: Name two tools to measure a map.
PQthread laid along the riverthe same thread, straightened020406080100km

In the figure : In the figure a thread laid along a curved river or road and then straightened can be measured against the scale (sample values).

Live figure

Verbal, numerical and linear (graphical) scales

In the app you can move this figure with your finger.

Open in the app
  • Easy : Easy: A thread measures a curved river.
  • Medium : Medium: Straightened thread 7 cm at 1 cm = 20 km → 140 km.
  • Exam-type : Exam: Why is a thread used for curves?
Remember

Three scales: verbal, numerical (RF), linear.

Common mistake

Writing units in RF. RF has none.

Shortcut

Memory clue: "शब्द - संख्या - रेषा".

Spot the difference

KindExampleUnits
Verbal1 cm = 60 kmcm, km
Numerical1:60,00,000None
LinearLine with 0, 60, 120km

Practice questions

Easy
  1. 1Name the three kinds of scale.
  2. 2What is RF?
  3. 3Which side of a scale is the map?
Medium
  1. 4Which scale has no units?
  2. 5What can measure a curved road?
  3. 6Write "1 cm = 60 km" as a linear scale up to 180 km.
Challenging
  1. 7A thread is 9 cm on a 1 cm = 10 km map. Find the length of the river.
  2. 8Why is the numerical scale good for global maps?
Show answers (try them yourself first)
  1. 1Verbal, numerical, linear.
  2. 2Representative Fraction, the numerical scale.
  3. 3The left side.
  4. 4Numerical.
  5. 5A thread.
  6. 6A 3 cm line marked 0, 60, 120, 180.
  7. 79 × 10 = 90 km.
  8. 8It has no units, so every country can use it.

Graphical scale, reducing/enlarging maps and measuring distances

From daily life

Copy a map at 50% on a photocopier and the village looks smaller, but the words "1 cm = 10 km" printed on it stay the same and are now wrong. A drawn scale bar shrinks along with it.

Simple definition

A graphical scale (आलेखीय प्रमाण) stays correct when a map is reduced or enlarged, because it changes with the map.

Rule 1: Reducing and enlarging — A map may be reduced or enlarged (e.g. photocopying). The verbal and numerical scales do not change on the copy, so they become wrong; the graphical scale changes with the map and stays right. So atlases and wall maps carry graphical scales.

AOriginalprinted scale:1 cm = 20 km02040kmBPhotocopyprinted scale:1 cm = 20 km02040km

In the figure : In the figure when a map is reduced or enlarged, the verbal and numerical scales become wrong, but the graphical scale changes along with the map and stays correct.

  • Easy : Easy: Graphical scale stays right.
  • Medium : Medium: At half size, a 1 cm = 10 km map becomes 1 cm = 20 km.
  • Exam-type : Exam: Why do atlases use graphical scales?

Rule 2: Measuring on plans — University map: if the statue and gate are 0.5 km apart, measure the map distance and find the scale. Plan layout: with 1 cm = 1 km, measure along the roads to find distances from the shopping mall. Use a thread for a river's length.

1.5 cm2 cm1.5 cm2.5 cmParkMallHospitalSchoolScale: 1 cm = 2 km

In the figure : In the figure distances from a place are found by measuring along the roads and using the scale (sample plan).

  • Easy : Easy: Measure along the road.
  • Medium : Medium: Road of 4.5 cm at 1 cm = 1 km is 4.5 km.
  • Exam-type : Exam: A 0.5 km distance is 2.5 cm on a map. Find the scale. 0.5 km = 50,000 cm; 50,000 ÷ 2.5 = 20,000, so 1:20,000.
Remember

Graphical scale survives reduction/enlargement.

Common mistake

Trusting the written scale on a photocopy. It may be wrong.

Shortcut

Memory clue: "रेषा लहान तर प्रमाण लहान".

Spot the difference

ScaleAfter copying
VerbalWrong
NumericalWrong
GraphicalCorrect

Practice questions

Easy
  1. 1Which scale stays correct after copying?
  2. 2Why do verbal scales become wrong?
  3. 3Where are graphical scales drawn?
Medium
  1. 4What do we use for a river?
  2. 5A map is enlarged to double. What happens to 1 cm = 10 km?
  3. 6Why must we measure along roads on a plan?
Challenging
  1. 75 cm road at 1 cm = 2 km. Real length?
  2. 8Why does an enlarged copy change the scale?
Show answers (try them yourself first)
  1. 1Graphical.
  2. 2The words do not change when the map size changes.
  3. 3Atlases and wall maps.
  4. 4A thread.
  5. 5It becomes 1 cm = 5 km.
  6. 6We travel along them.
  7. 710 km.
  8. 8The same ground distance now covers more paper.

Large scale and small scale maps

From daily life

A class map shows every desk, but a world map in an atlas shows only countries. A small piece of ground drawn big gives detail; a big piece drawn small does not.

Simple definition

A large scale map (मोठ्या प्रमाणाचा नकाशा) shows a small area in more detail; a small scale map (लहान प्रमाणाचा) shows a large area in less detail.

Rule 1: Large and small scale — Large scale: a small ground area covers a large map area; more detail; village, school, fields, city maps. Small scale: a large ground area covers a small map area; less detail; atlas, country, continent, world maps. 1 cm = 100 m is large scale; 1 cm = 100 km is small scale. The village symbol gets smaller as the scale gets smaller.

1:10,0001:1,00,0001:10,00,000

In the figure : In the figure large scale map: a small area in more detail (village, school, city). Small scale map: a large area in less detail (atlas, country, world).

  • Easy : Easy: A school map is large scale.
  • Medium : Medium: A world map is small scale.
  • Exam-type : Exam: Compare large and small scale.

Rule 2: Comparing ratios — Ratios compare like fractions: the smaller the denominator, the larger the fraction. So 1:10,000 is large scale and 1:50,000 is small scale. In the list 1:1,000, 1:2,500, 1:5,000, 1:25,000, 1:50,000, 1:1,00,000, 1:2,50,000, 1:10,00,000, the first are large and the last are small.

ABLarge scale mapSmall scale map

In the figure : In the figure the symbol of a village becomes smaller as the scale gets smaller; 1:10,000 is a larger scale than 1:50,000 because 1/10,000 is a larger fraction.

  • Easy : Easy: 1:5,000 is larger than 1:25,000.
  • Medium : Medium: 1/5,000 is 5 times 1/25,000.
  • Exam-type : Exam: Which is larger: 1:50,000 or 1:2,50,000?
Remember

Large scale = small area, more detail. Small scale = large area, less detail.

Common mistake

Thinking a bigger number in the ratio means a larger scale. It is the opposite.

Shortcut

Memory clue: "छेद लहान = प्रमाण मोठे".

Spot the difference

Scale typeAreaDetailExample
LargeSmallMoreVillage map
SmallLargeLessWorld map

Practice questions

Easy
  1. 1What is a large scale map?
  2. 2Give two examples.
  3. 3What is a small scale map?
Medium
  1. 4Is an atlas map large or small scale?
  2. 5Which is larger: 1:10,000 or 1:50,000?
  3. 6Is 1 cm = 100 m large or small scale?
Challenging
  1. 7Arrange from large to small: 1:1,00,000, 1:5,000, 1:25,000.
  2. 8Why do small scale maps show fewer details?
Show answers (try them yourself first)
  1. 1A map showing a small area in detail.
  2. 2Village and school maps.
  3. 3A map showing a large area with less detail.
  4. 4Small scale.
  5. 51:10,000.
  6. 6Large.
  7. 71:5,000, 1:25,000, 1:1,00,000.
  8. 8A huge area is squeezed into little space.

Converting scales and calculating distances

From daily life

When you plan a trip you ask "how far, and how much will it cost?" Both answers come from the map scale: distance first, then cost.

Simple definition

To convert a scale, change the units to centimetres (1 km = 1,00,000 cm); then ground distance = map distance × scale.

Rule 1: Verbal to numerical and back — Verbal → numerical: 1 cm = 25 km = 25 × 1,00,000 cm → 1:25,00,000. Numerical → verbal: 1:20,00,000 means 1 cm = 20,00,000 cm = 20 km → 1 cm = 20 km.

1 cm =45 km45 km =45,00,000cm1 :45,00,000

In the figure : In the figure verbal to numerical: change the ground distance into centimetres (1 km = 1,00,000 cm) and write the ratio without units (sample values).

  • Easy : Easy: 1 km = 1,00,000 cm.
  • Medium : Medium: 1 cm = 3 km → 1:3,00,000.
  • Exam-type : Exam: Convert 1 cm = 40 km. 40 × 1,00,000 = 40,00,000, so 1:40,00,000.
1 :2,00,0001 cm =2,00,000cm1 cm =2 km

In the figure : In the figure numerical to verbal: change the large number of centimetres into kilometres (divide by 1,00,000), here 1 cm = 2 km (sample values).

  • Easy : Easy: Divide by 1,00,000.
  • Medium : Medium: 1:2,00,000 → 2 km per cm.
  • Exam-type : Exam: Convert 1:5,00,000. 5,00,000 ÷ 1,00,000 = 5, so 1 cm = 5 km.

Rule 2: Distance and cost — Ground distance = map distance × scale: 6 cm at 1 cm = 8 km gives 48 km. Showing a distance: 2 km drawn as 4 cm → 1 cm = 0.5 km = 50,000 cm → 1:50,000. A 300 km road with a scale line of 50 km per unit is drawn 300 ÷ 50 = 6 units long. Trip cost = distance × rate per km; for a to-and-fro journey, double the one-way distance: 40 km each way = 80 km × Rs 12 = Rs 960. Project: draw a scale plan of your school and use Google Maps to find the distance between two villages, showing all three scales.

012345678XYScale: 1 cm = 15 km

In the figure : In the figure ground distance = map distance × scale: 3 cm at 1 cm = 15 km is 45 km (sample values).

  • Easy : Easy: 3 × 15 = 45 km.
  • Medium : Medium: 8 cm at 1 cm = 5 km → 40 km.
  • Exam-type : Exam: A map has 1 cm = 12 km. Find 7.5 cm. 7.5 × 12 = 90 km.
Distance of a journey (sample values)One way80 kmTo and fro160 km

In the figure : In the figure for a to-and-fro journey, double the one-way distance; trip cost = distance × rate per km (sample values).

  • Easy : Easy: Round trip = 2 × one-way.
  • Medium : Medium: 25 km one-way, round trip 50 km.
  • Exam-type : Exam: Cost for 50 km at Rs 10/km? 50 × 10 = Rs 500.
Remember

1 km = 1,00,000 cm. Ground = map × scale. Round trip doubles.

Common mistake

Forgetting to convert km to cm. Convert first.

Shortcut

Memory clue: "km × 1,00,000 = cm".

Spot the difference

ConversionMethod
Verbal → numericalkm × 1,00,000
Numerical → verbal÷ 1,00,000
Ground distanceMap × scale

Practice questions

Easy
  1. 1How many cm are in 1 km?
  2. 2Convert 1 cm = 10 km.
  3. 3Convert 1:1,00,00,000.
Medium
  1. 4Formula of ground distance?
  2. 54 cm on a 1 cm = 25 km map. Ground?
  3. 61 km is shown by 5 cm. Find the RF.
Challenging
  1. 7Two villages are 6.5 cm apart at 1:5,00,000. Real distance?
  2. 8A bus goes 60 km each way at Rs 9/km. Round-trip cost?
Show answers (try them yourself first)
  1. 11,00,000.
  2. 21:10,00,000.
  3. 31 cm = 100 km.
  4. 4Map distance × scale.
  5. 5100 km.
  6. 61 km = 1,00,000 cm; 1,00,000 ÷ 5 = 20,000; 1:20,000.
  7. 76.5 × 5 = 32.5 km.
  8. 8120 × 9 = Rs 1080.

Quick revision

  • Map scale = map distance : ground distance. Three kinds: verbal, numerical (RF), linear (graphical).
  • Numerical scale is global (no units). Graphical scale stays correct when a map is reduced or enlarged.
  • Large scale: small area, more detail (village, school); small scale: large area, less detail (atlas, world). 1:10,000 is larger than 1:50,000.
  • Conversions: 1 km = 1,00,000 cm. 1 cm = 53 km → 1:53,00,000. 1:1,00,00,000 → 1 cm = 100 km.
  • Ground distance = map distance × scale; use thread or compass for measuring.