Chapter 6 of 14
Chapter 6: Measuring Length
Centimetres, Metres, Kilometres, Conversions & Perimeter of Shapes | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Metric units of length: millimetre (mm), centimetre (cm), metre (m), and kilometre (km).
- Key conversion relationships: 1 m = 100 cm; 1 km = 1,000 m; 1 cm = 10 mm.
- Measuring curved paths using a string and ruler.
- Calculating perimeter (total boundary length) by summing the lengths of all outer sides.
All Textbook Exercises & In-Text Tasks (15 Questions)
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Q1
Metric Unit Conversions
Convert the following: (a) 4 metres 65 centimetres into cm; (b) 7,500 metres into kilometres and metres; (c) 8 kilometres 40 metres into metres.
[3 Marks]
✅ Step-by-Step Solution & Working
(a) 4 m 65 cm into cm:
• Since 1 m = 100 cm, 4 m = 4 × 100 = 400 cm.
• Total = 400 cm + 65 cm = 465 cm.
(b) 7,500 m into km and m:
• Since 1,000 m = 1 km, divide 7,500 by 1,000.
• 7,500 m = 7,000 m + 500 m = 7 km 500 m.
(c) 8 km 40 m into m:
• Since 1 km = 1,000 m, 8 km = 8 × 1,000 = 8,000 m.
• Total = 8,000 m + 40 m = 8,040 m (be careful not to write 8,400 m!).
• Since 1 m = 100 cm, 4 m = 4 × 100 = 400 cm.
• Total = 400 cm + 65 cm = 465 cm.
(b) 7,500 m into km and m:
• Since 1,000 m = 1 km, divide 7,500 by 1,000.
• 7,500 m = 7,000 m + 500 m = 7 km 500 m.
(c) 8 km 40 m into m:
• Since 1 km = 1,000 m, 8 km = 8 × 1,000 = 8,000 m.
• Total = 8,000 m + 40 m = 8,040 m (be careful not to write 8,400 m!).
CBSE Step-by-Step Marking Scheme
Correct conversion for (a)
1.0 M
Correct conversion for (b)
1.0 M
Correct conversion for (c) with zero placeholder
1.0 M
Q2
Perimeter Word Problem
A rectangular playground is 35 metres long and 20 metres wide. An athlete runs around the boundary 4 times every morning. What is the total distance run by the athlete in metres and kilometres?
[3 Marks]
✅ Step-by-Step Solution & Working
Step 1: Calculate the perimeter of the playground:
• Formula: Perimeter = 2 × (Length + Width)
• Perimeter = 2 × (35 m + 20 m) = 2 × 55 m = 110 metres.
(One full round = 110 m).
Step 2: Calculate distance for 4 rounds:
• Total distance = 4 × 110 m = 440 metres.
Step 3: Convert into kilometres:
• 440 m = 440 ÷ 1,000 = 0.44 km.
• Formula: Perimeter = 2 × (Length + Width)
• Perimeter = 2 × (35 m + 20 m) = 2 × 55 m = 110 metres.
(One full round = 110 m).
Step 2: Calculate distance for 4 rounds:
• Total distance = 4 × 110 m = 440 metres.
Step 3: Convert into kilometres:
• 440 m = 440 ÷ 1,000 = 0.44 km.
CBSE Step-by-Step Marking Scheme
Perimeter calculation of 110 m
1.5 M
Total 4 rounds distance 440 m and km conversion
1.5 M
Q3
Geometry • Perimeter Calculation
A rectangular school playground is 45 metres long and 30 metres wide. (a) What is its perimeter? (b) If an athlete runs 3 complete rounds around it, what total distance does she run?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Calculation:
Length (l) = 45 m, Breadth (b) = 30 m
1. Perimeter of the Playground:
Perimeter = 2 × (Length + Breadth)
= 2 × (45 m + 30 m) = 2 × 75 m = 150 metres.
2. Total Distance for 3 Rounds:
Distance = 3 × Perimeter = 3 × 150 m = 450 metres.
Length (l) = 45 m, Breadth (b) = 30 m
1. Perimeter of the Playground:
Perimeter = 2 × (Length + Breadth)
= 2 × (45 m + 30 m) = 2 × 75 m = 150 metres.
2. Total Distance for 3 Rounds:
Distance = 3 × Perimeter = 3 × 150 m = 450 metres.
CBSE Step-by-Step Marking Scheme
Perimeter formula and correct answer (150 m)
1.5 M
Multiplication by 3 rounds (450 m)
1.5 M
Q4
Unit Conversions • Metres & Kilometres
Convert: (a) 4,250 metres into kilometres and metres, (b) 7 kilometres 85 metres into metres.
[2 Marks]
✅ Step-by-Step Solution & Working
Conversions (1 km = 1,000 m):
• (a) 4,250 m:
4,250 ÷ 1,000 = 4 km and 250 m.
• (b) 7 km 85 m:
(7 × 1,000 m) + 85 m = 7,000 m + 85 m = 7,085 m.
• (a) 4,250 m:
4,250 ÷ 1,000 = 4 km and 250 m.
• (b) 7 km 85 m:
(7 × 1,000 m) + 85 m = 7,000 m + 85 m = 7,085 m.
CBSE Step-by-Step Marking Scheme
Part (a): 4 km 250 m
1.0 M
Part (b): 7,085 m
1.0 M
Q5
Textbook Exercise • Real-World Context
In Chapter 6 ('Measuring Length'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Practice Time • Measurement & Conversions
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams.
[3 Marks]
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams.
✅ Step-by-Step Solution & Working
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Try These • Geometry and Shapes
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have?
[3 Marks]
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have?
✅ Step-by-Step Solution & Working
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
Money & Accounts • Rate List Calculation
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns?
[3 Marks]
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns?
✅ Step-by-Step Solution & Working
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
Fractions Exploration • Parts of a Whole
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena?
[3 Marks]
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena?
✅ Step-by-Step Solution & Working
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
Time & Clocks • Elapsed Time
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last?
[3 Marks]
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last?
✅ Step-by-Step Solution & Working
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
Perimeter & Area • Fencing a Field
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing.
[3 Marks]
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing.
✅ Step-by-Step Solution & Working
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Mental Math • Division and Multiplication
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ?
[2 Marks]
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ?
✅ Step-by-Step Solution & Working
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Patterns & Symmetries • Rotational Turns
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)?
[2 Marks]
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)?
✅ Step-by-Step Solution & Working
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
Smart Charts • Data Interpretation
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data.
[3 Marks]
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data.
✅ Step-by-Step Solution & Working
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
Chapter Review • True or False
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth).
[3 Marks]
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth).
✅ Step-by-Step Solution & Working
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study
School Boundary Fencing Budget
The school management needs to put a wire fence around a square herb garden measuring 15 metres on each side. The fencing contractor charges ₹40 per metre of wire.
Analytical Task: Calculate: (a) The total length of wire needed for 1 round of fence, (b) The total cost of fencing.
Evaluation & Model Answer:
(a) Length of wire:
Perimeter of square garden = 4 × side = 4 × 15 m = 60 metres.
(b) Total Cost:
Cost = 60 m × ₹40/m = ₹2,400.
Perimeter of square garden = 4 × side = 4 × 15 m = 60 metres.
(b) Total Cost:
Cost = 60 m × ₹40/m = ₹2,400.
Rubric: 1 Mark for perimeter 60 m; 1 Mark for multiplying rate to get ₹2,400.