Chapter 14 of 14
Chapter 14: How Big? How Heavy?
कितना बड़ा? कितना भारी? (आयतन, घन सेमी, जल विस्थापन एवं भार तुलना) | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Volume is the 3D space occupied by an object: Volume of Cuboid = Length × Breadth × Height.
- Standard unit of volume: Cubic centimetre (cu cm or cm³).
- Water displacement method: Volume of an irregular solid = Volume of water displaced.
- Packing volume: Number of small unit cubes that can fit into a larger carton box.
- Given: Volume displaced by 6 marbles = 12 ml.
All Textbook Exercises & In-Text Tasks (24 Questions)
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Q1
Textbook Exercise • Measuring Volume with Marbles
A measuring glass filled with water to 50 mL mark rises to 68 mL when 9 equal glass marbles are dropped inside.
(a) How much water was displaced by all 9 marbles?
(b) What is the volume of 1 marble in mL?
(c) What is the volume in cubic centimetres (cm³) if 1 mL = 1 cm³?
[3 Marks]
(a) How much water was displaced by all 9 marbles?
(b) What is the volume of 1 marble in mL?
(c) What is the volume in cubic centimetres (cm³) if 1 mL = 1 cm³?
✅ Step-by-Step Solution & Working
Volume by Water Displacement:
• (a) Displaced water: 68 mL - 50 mL = 18 mL.
• (b) Volume of 1 marble: 18 mL ÷ 9 marbles = 2 mL.
• (c) In cubic centimetres: 2 mL = 2 cm³.
• (a) Displaced water: 68 mL - 50 mL = 18 mL.
• (b) Volume of 1 marble: 18 mL ÷ 9 marbles = 2 mL.
• (c) In cubic centimetres: 2 mL = 2 cm³.
CBSE Step-by-Step Marking Scheme
Part (a): 18 mL
1 M
Part (b): 2 mL
1 M
Part (c): 2 cm³
1 M
Q2
Textbook Exercise • Volume of a Cube
(a) What is the formula for the volume of a cube? (b) Find the volume of a wooden cube of side 5 cm. (c) How many 1 cm unit cubes can fit inside it?
[3 Marks]
✅ Step-by-Step Solution & Working
Volume of Cube:
• (a) Formula: Volume = Side × Side × Side = Side³.
• (b) Volume: 5 cm × 5 cm × 5 cm = 125 cm³.
• (c) Number of 1 cm unit cubes: 125 ÷ 1 = 125 cubes.
• (a) Formula: Volume = Side × Side × Side = Side³.
• (b) Volume: 5 cm × 5 cm × 5 cm = 125 cm³.
• (c) Number of 1 cm unit cubes: 125 ÷ 1 = 125 cubes.
CBSE Step-by-Step Marking Scheme
Formula: Side³
1 M
Volume: 125 cm³
1 M
125 unit cubes fit
1 M
Q3
Textbook Exercise • Volume of a Cuboid
A matchbox measures 5 cm in length, 3 cm in width, and 1 cm in height. (a) What is the volume of one matchbox? (b) What is the volume of a packet containing 12 such matchboxes?
[3 Marks]
✅ Step-by-Step Solution & Working
Volume Calculations (Volume = l × w × h):
• (a) One matchbox: 5 cm × 3 cm × 1 cm = 15 cm³.
• (b) Packet of 12 matchboxes: 12 × 15 cm³ = 180 cm³.
• (a) One matchbox: 5 cm × 3 cm × 1 cm = 15 cm³.
• (b) Packet of 12 matchboxes: 12 × 15 cm³ = 180 cm³.
CBSE Step-by-Step Marking Scheme
One matchbox: 15 cm³
1.5 M
Packet: 180 cm³
1.5 M
Q4
Textbook Exercise • Packing Cubes into a Carton
A carton box is 20 cm long, 10 cm wide, and 8 cm high. How many soap cakes of size 5 cm × 5 cm × 4 cm can be packed inside the carton box?
[3 Marks]
✅ Step-by-Step Solution & Working
Packing Capacity:
• Method 1 (Dimensions fitting):
- Along 20 cm length: 20 ÷ 5 = 4 soaps.
- Along 10 cm width: 10 ÷ 5 = 2 soaps.
- Along 8 cm height: 8 ÷ 4 = 2 soaps.
- Total soaps = 4 × 2 × 2 = 16 soaps.
• Method 2 (Volume): Volume of carton = 20 × 10 × 8 = 1,600 cm³. Volume of 1 soap = 5 × 5 × 4 = 100 cm³. Number of soaps = 1,600 ÷ 100 = 16 soaps.
• Method 1 (Dimensions fitting):
- Along 20 cm length: 20 ÷ 5 = 4 soaps.
- Along 10 cm width: 10 ÷ 5 = 2 soaps.
- Along 8 cm height: 8 ÷ 4 = 2 soaps.
- Total soaps = 4 × 2 × 2 = 16 soaps.
• Method 2 (Volume): Volume of carton = 20 × 10 × 8 = 1,600 cm³. Volume of 1 soap = 5 × 5 × 4 = 100 cm³. Number of soaps = 1,600 ÷ 100 = 16 soaps.
CBSE Step-by-Step Marking Scheme
Dimension fitting / Volume method
1.5 M
Answer: 16 soaps
1.5 M
Q5
Textbook Exercise • Stage Building with Matchboxes
Tanu made a stage using 14 matchboxes in one layer. She built a platform 3 layers high. (a) How many matchboxes did she use in total? (b) If each matchbox has volume 15 cm³, what is the total volume of the stage platform?
[3 Marks]
✅ Step-by-Step Solution & Working
Stage Platform Calculations:
• (a) Total matchboxes: 14 matchboxes/layer × 3 layers = 42 matchboxes.
• (b) Total volume: 42 × 15 cm³ = 630 cm³.
• (a) Total matchboxes: 14 matchboxes/layer × 3 layers = 42 matchboxes.
• (b) Total volume: 42 × 15 cm³ = 630 cm³.
CBSE Step-by-Step Marking Scheme
Total matchboxes: 42
1.5 M
Total volume: 630 cm³
1.5 M
Q6
Textbook Exercise • Weight of Coins (5-Rupee Coin)
A ₹5 coin weighs 9 grams. A bank sack full of ₹5 coins weighs 9 kilograms. (a) Convert 9 kg into grams. (b) How many ₹5 coins are in the sack? (c) What is the total monetary value of all the coins in the sack?
[3 Marks]
✅ Step-by-Step Solution & Working
Coin & Weight Calculations:
• (a) Conversion: 9 kg = 9 × 1,000 = 9,000 grams.
• (b) Number of coins: 9,000 g ÷ 9 g/coin = 1,000 coins.
• (c) Monetary value: 1,000 coins × ₹5 = ₹5,000.
• (a) Conversion: 9 kg = 9 × 1,000 = 9,000 grams.
• (b) Number of coins: 9,000 g ÷ 9 g/coin = 1,000 coins.
• (c) Monetary value: 1,000 coins × ₹5 = ₹5,000.
CBSE Step-by-Step Marking Scheme
9,000 grams
1 M
1,000 coins
1 M
Value: ₹5,000
1 M
Q7
Textbook Exercise • 2-Rupee Coin Sack Weight
A ₹2 coin weighs 6 grams. A sack containing ₹2 coins weighs 4 kg and 800 grams. How many ₹2 coins are inside the sack?
[3 Marks]
✅ Step-by-Step Solution & Working
Weight Conversion & Division:
1. Total weight in grams = 4,000 g + 800 g = 4,800 grams.
2. Weight of 1 coin = 6 grams.
3. Number of coins = 4,800 ÷ 6 = 800 coins.
1. Total weight in grams = 4,000 g + 800 g = 4,800 grams.
2. Weight of 1 coin = 6 grams.
3. Number of coins = 4,800 ÷ 6 = 800 coins.
CBSE Step-by-Step Marking Scheme
4,800 grams conversion
1.5 M
Answer: 800 coins
1.5 M
Q8
Textbook Exercise • Litres and Millilitres to Cubic Centimetres
Fill in the blanks: (a) 1 litre = _____ mL. (b) 1 mL = _____ cm³. (c) 1 litre = _____ cm³.
[3 Marks]
✅ Step-by-Step Solution & Working
Volume Equivalences:
• (a) 1 litre = 1,000 mL.
• (b) 1 mL = 1 cm³.
• (c) 1 litre = 1,000 mL = 1,000 cm³.
• (a) 1 litre = 1,000 mL.
• (b) 1 mL = 1 cm³.
• (c) 1 litre = 1,000 mL = 1,000 cm³.
CBSE Step-by-Step Marking Scheme
1,000 mL
1 M
1 cm³
1 M
1,000 cm³
1 M
Q9
Textbook Exercise • Water Tank Capacity in Litres
A rectangular overhead water tank is 2 metres long, 1.5 metres wide, and 1 metre high. (a) What is its volume in cubic metres? (b) How many litres of water can it hold if 1 cubic metre (m³) = 1,000 litres?
[3 Marks]
✅ Step-by-Step Solution & Working
Tank Capacity:
• (a) Volume: 2 m × 1.5 m × 1 m = 3 cubic metres (3 m³).
• (b) Capacity in litres: 3 m³ × 1,000 litres/m³ = 3,000 litres.
• (a) Volume: 2 m × 1.5 m × 1 m = 3 cubic metres (3 m³).
• (b) Capacity in litres: 3 m³ × 1,000 litres/m³ = 3,000 litres.
CBSE Step-by-Step Marking Scheme
Volume: 3 m³
1.5 M
Capacity: 3,000 litres
1.5 M
Q10
Textbook Exercise • Heavy School Bag Weight
A student's school bag has: 4 textbooks weighing 350 g each, 5 notebooks weighing 150 g each, a water bottle weighing 800 g, and a pencil box weighing 250 g. What is the total weight of the bag in kg and g?
[3 Marks]
✅ Step-by-Step Solution & Working
Total Weight Calculation:
• Textbooks: 4 × 350 g = 1,400 g.
• Notebooks: 5 × 150 g = 750 g.
• Water bottle: 800 g.
• Pencil box: 250 g.
• Sum in grams: 1,400 + 750 + 800 + 250 = 3,200 grams.
• In kg and g = 3 kg and 200 grams (3.2 kg).
• Textbooks: 4 × 350 g = 1,400 g.
• Notebooks: 5 × 150 g = 750 g.
• Water bottle: 800 g.
• Pencil box: 250 g.
• Sum in grams: 1,400 + 750 + 800 + 250 = 3,200 grams.
• In kg and g = 3 kg and 200 grams (3.2 kg).
CBSE Step-by-Step Marking Scheme
Itemized weights calculated
1.5 M
Total: 3 kg 200 g
1.5 M
Q11
Textbook Exercise • Comparing Volumes of Liquid & Solid
A solid metal cube of side 4 cm is dropped into a full container of water. How many millilitres of water will overflow?
[2 Marks]
✅ Step-by-Step Solution & Working
Water Displacement Principle:
• A submerged solid displaces an amount of water equal to its own volume.
• Volume of metal cube = 4 cm × 4 cm × 4 cm = 64 cm³.
• Since 1 cm³ = 1 mL, the volume of water displaced = 64 mL.
Therefore, 64 mL of water will overflow.
• A submerged solid displaces an amount of water equal to its own volume.
• Volume of metal cube = 4 cm × 4 cm × 4 cm = 64 cm³.
• Since 1 cm³ = 1 mL, the volume of water displaced = 64 mL.
Therefore, 64 mL of water will overflow.
CBSE Step-by-Step Marking Scheme
Volume of cube = 64 cm³
1 M
Overflow = 64 mL
1 M
Q12
Textbook Exercise • Cardboard Box Volume
Find the volume of a cardboard box that is 45 cm long, 25 cm wide, and 20 cm high.
[2 Marks]
✅ Step-by-Step Solution & Working
Volume Calculation:
• Volume = Length × Width × Height = 45 × 25 × 20 cm³.
• 25 × 20 = 500.
• 45 × 500 = 22,500 cm³.
• Volume = Length × Width × Height = 45 × 25 × 20 cm³.
• 25 × 20 = 500.
• 45 × 500 = 22,500 cm³.
CBSE Step-by-Step Marking Scheme
Formula l × w × h
1 M
Answer: 22,500 cm³
1 M
Q13
Textbook Exercise • Rice Grain Count Estimation
100 grains of rice weigh about 2 grams. (a) What is the weight of 1 grain of rice? (b) Approximately how many grains of rice are there in a 1 kg (1,000 g) bag?
[3 Marks]
✅ Step-by-Step Solution & Working
Estimation:
• (a) Weight of 1 grain: 2 g ÷ 100 = 0.02 grams.
• (b) Grains in 1 kg: 1,000 g ÷ 2 g = 500 packets of 100 grains.
Total grains = 500 × 100 = 50,000 grains.
• (a) Weight of 1 grain: 2 g ÷ 100 = 0.02 grams.
• (b) Grains in 1 kg: 1,000 g ÷ 2 g = 500 packets of 100 grains.
Total grains = 500 × 100 = 50,000 grains.
CBSE Step-by-Step Marking Scheme
1 grain: 0.02 g
1 M
1 kg has 50,000 grains
2 M
Q14
Textbook Exercise • Cubes from a Large Wooden Block
A rectangular wooden block is 12 cm × 9 cm × 6 cm. It is cut into small cubes of side 3 cm. How many small cubes can be cut without any wood wasted?
[2 Marks]
✅ Step-by-Step Solution & Working
Cube Division:
• Along length: 12 ÷ 3 = 4 cubes.
• Along width: 9 ÷ 3 = 3 cubes.
• Along height: 6 ÷ 3 = 2 cubes.
• Total cubes: 4 × 3 × 2 = 24 cubes.
• Along length: 12 ÷ 3 = 4 cubes.
• Along width: 9 ÷ 3 = 3 cubes.
• Along height: 6 ÷ 3 = 2 cubes.
• Total cubes: 4 × 3 × 2 = 24 cubes.
CBSE Step-by-Step Marking Scheme
Dimensions division (4 × 3 × 2)
1 M
Total: 24 cubes
1 M
Q15
Textbook Exercise • Juice Carton Content
A juice pack is a rectangular cuboid measuring 10 cm × 6 cm × 15 cm. (a) What is its volume in cm³? (b) How many litres of juice does it contain (assuming full)?
[2 Marks]
✅ Step-by-Step Solution & Working
Volume & Capacity:
• (a) Volume: 10 × 6 × 15 = 900 cm³.
• (b) Capacity in litres: 900 cm³ = 900 mL = 900 ÷ 1,000 = 0.9 litres.
• (a) Volume: 10 × 6 × 15 = 900 cm³.
• (b) Capacity in litres: 900 cm³ = 900 mL = 900 ÷ 1,000 = 0.9 litres.
CBSE Step-by-Step Marking Scheme
Volume: 900 cm³
1 M
Capacity: 0.9 litres
1 M
Q16
Textbook Exercise • Doubling Cube Side (Volume Effect)
A cube has side 2 cm. If its side is doubled to 4 cm: (a) Find original volume. (b) Find new volume. (c) By how many times does the volume increase?
[3 Marks]
✅ Step-by-Step Solution & Working
Volume Scaling:
• (a) Original: 2 × 2 × 2 = 8 cm³.
• (b) New: 4 × 4 × 4 = 64 cm³.
• (c) Increase factor: 64 ÷ 8 = 8 times larger (since 2³ = 8).
• (a) Original: 2 × 2 × 2 = 8 cm³.
• (b) New: 4 × 4 × 4 = 64 cm³.
• (c) Increase factor: 64 ÷ 8 = 8 times larger (since 2³ = 8).
CBSE Step-by-Step Marking Scheme
Original: 8 cm³
1 M
New: 64 cm³
1 M
Increases by 8 times
1 M
Q17
Textbook Exercise • Ice Cube Melting Volume
An ice cube has side 3 cm. When melted, does water occupy more, less, or equal volume to ice? (Scientific note: Ice expands when frozen; 100 cm³ ice produces ~92 mL water).
[2 Marks]
✅ Step-by-Step Solution & Working
Observation:
• Volume of ice cube = 3 × 3 × 3 = 27 cm³.
• Water occupies slightly less volume than ice because water expands when freezing. When 27 cm³ of ice melts, it produces about 25 mL of liquid water.
• Volume of ice cube = 3 × 3 × 3 = 27 cm³.
• Water occupies slightly less volume than ice because water expands when freezing. When 27 cm³ of ice melts, it produces about 25 mL of liquid water.
CBSE Step-by-Step Marking Scheme
Volume calculation: 27 cm³
1 M
Water occupies less volume explained
1 M
Q18
Textbook Exercise • Soil Dug from a Pit
A pit 4 metres long, 3 metres wide, and 2 metres deep is dug in a field. How many cubic metres of earth (soil) were dug out?
[2 Marks]
✅ Step-by-Step Solution & Working
Volume of Excavation:
• Volume of earth dug = Length × Width × Depth = 4 m × 3 m × 2 m = 24 cubic metres (24 m³).
• Volume of earth dug = Length × Width × Depth = 4 m × 3 m × 2 m = 24 cubic metres (24 m³).
CBSE Step-by-Step Marking Scheme
Formula l × w × d
1 M
Answer: 24 m³
1 M
Q19
Textbook Exercise • Difference between Weight and Volume
Explain why 1 kg of cotton wool occupies a much larger volume (space) than 1 kg of iron, even though their weights are equal.
[2 Marks]
✅ Step-by-Step Solution & Working
Density & Volume:
• Both have the exact same weight (1 kg).
• However, iron is very dense with closely packed particles, so 1 kg fits in a small space.
• Cotton is fluffy, porous, and contains a lot of trapped air, meaning its particles are loosely spread, so 1 kg occupies a huge physical space (large volume).
• Both have the exact same weight (1 kg).
• However, iron is very dense with closely packed particles, so 1 kg fits in a small space.
• Cotton is fluffy, porous, and contains a lot of trapped air, meaning its particles are loosely spread, so 1 kg occupies a huge physical space (large volume).
CBSE Step-by-Step Marking Scheme
Equal mass/weight stated
1 M
Density & particle spacing explained
1 M
Q20
Textbook Exercise • Weight of 100 One-Rupee Coins
A 1-rupee coin weighs 4.85 grams. What is the total weight of 100 such 1-rupee coins in grams?
[2 Marks]
✅ Step-by-Step Solution & Working
Multiplication:
• Total weight = 100 × 4.85 g = 485 grams.
• Total weight = 100 × 4.85 g = 485 grams.
CBSE Step-by-Step Marking Scheme
Multiplication 100 × 4.85
1 M
Answer: 485 grams
1 M
Q21
Textbook Exercise • Swimming Pool Capacity
A small rectangular children's pool is 10 m long, 5 m wide, and 1.2 m deep. What is the total volume of water needed to fill it to the brim in litres?
[3 Marks]
✅ Step-by-Step Solution & Working
Volume and Litres:
• Volume = 10 × 5 × 1.2 = 60 cubic metres.
• In litres = 60 × 1,000 litres = 60,000 litres.
• Volume = 10 × 5 × 1.2 = 60 cubic metres.
• In litres = 60 × 1,000 litres = 60,000 litres.
CBSE Step-by-Step Marking Scheme
Volume: 60 m³
1.5 M
Capacity: 60,000 litres
1.5 M
Q22
Textbook Exercise • Brick Stacking Volume
A standard construction brick measures 20 cm × 10 cm × 8 cm. Find the volume of a stack containing 500 such bricks in cubic metres.
[3 Marks]
✅ Step-by-Step Solution & Working
Brick Stack Volume:
• Volume of 1 brick = 20 × 10 × 8 = 1,600 cm³.
• Volume of 500 bricks = 500 × 1,600 = 800,000 cm³.
• In cubic metres: 1 m³ = 1,000,000 cm³.
• Volume = 800,000 ÷ 1,000,000 = 0.8 m³.
• Volume of 1 brick = 20 × 10 × 8 = 1,600 cm³.
• Volume of 500 bricks = 500 × 1,600 = 800,000 cm³.
• In cubic metres: 1 m³ = 1,000,000 cm³.
• Volume = 800,000 ÷ 1,000,000 = 0.8 m³.
CBSE Step-by-Step Marking Scheme
1 brick: 1,600 cm³
1 M
500 bricks: 800,000 cm³
1 M
Converted to 0.8 m³
1 M
Q23
Textbook Exercise • Balance Scale Weighing
On a two-pan balance scale, a watermelon on the left pan balances with: one 2 kg weight, one 500 g weight, and two 200 g weights on the right pan. What is the weight of the watermelon?
[2 Marks]
✅ Step-by-Step Solution & Working
Weight Balance:
• 2 kg = 2,000 g.
• Weights on right pan = 2,000 + 500 + 200 + 200 = 2,900 grams (or 2 kg 900 g).
• 2 kg = 2,000 g.
• Weights on right pan = 2,000 + 500 + 200 + 200 = 2,900 grams (or 2 kg 900 g).
CBSE Step-by-Step Marking Scheme
Sum of weights on pan
1 M
Watermelon weight: 2 kg 900 g
1 M
Q24
Textbook Exercise • Measuring Cylinder Meniscus
When reading the liquid level in a measuring cylinder, why should your eye be level with the bottom of the curved water surface (meniscus)?
[2 Marks]
✅ Step-by-Step Solution & Working
Accurate Measurement:
• Due to surface tension, water curves upwards slightly at the container edges, forming a concave curved surface called a meniscus.
• Looking from above or below introduces parallax error. Keeping your eye directly level with the lowest point of the meniscus ensures an accurate and true volume reading.
• Due to surface tension, water curves upwards slightly at the container edges, forming a concave curved surface called a meniscus.
• Looking from above or below introduces parallax error. Keeping your eye directly level with the lowest point of the meniscus ensures an accurate and true volume reading.
CBSE Step-by-Step Marking Scheme
Meniscus curvature explained
1 M
Avoiding parallax error explained
1 M
🌟 NEP 2020 Competency-Based Case Study
NEP 2020 Competency Case: How Big? How Heavy?
A practical scenario involving How Big? How Heavy? in everyday life and community contexts.
Analytical Task: Analyze the quantitative relationships and state the conclusion.
Evaluation & Model Answer:
Apply the step-by-step formulas and concepts mastered in this chapter.
Rubric: 1M formula + 1M working + 1M answer