Materials: Metals and Non-Metals – Numerical Problems with Stepwise Solutions
Class 8
Science — Chapter 4: Materials: Metals and Non-Metals
CBSE Board Examinations
Content Bank — Important formulas & relations (Chapter: Metals & Non-metals)
- Density (ρ) = mass (m) / volume (V). → ρ = m / V
- Mass = Density × Volume. → m = ρ × V
- Volume = Mass / Density. → V = m / ρ
- Percentage by mass = (part / whole) × 100%
- Percentage change = (change / original) × 100%
- Displacement method — volume of irregular solid = final water volume − initial water volume
- Mass of alloy component = total mass × fraction (or % /100)
Tip: Use density tables (e.g., density of iron ≈ 7.87 g/cm³, aluminium ≈ 2.70 g/cm³, copper ≈ 8.96 g/cm³) when needed — only if given in question or reference.
How to use these problems:
- Attempt problems topic-wise — first try without looking at solutions.
- Follow stepwise solutions to learn approach and reasoning.
- Use the content bank as a quick reference for formula application.
Topic: Density and Volume (1)
1. A solid metal cube has an edge length of 4 cm and mass 512 g. Calculate its density in g/cm³.
Step 1: Volume of cube, V = edge³ = 4³ = 64 cm³.
Step 2: Density, ρ = mass / volume = 512 g / 64 cm³ = 8 g/cm³.
Answer: 8 g/cm³.
Topic: Density and Volume (2)
2. A metal piece displaces water from 50.0 mL to 58.2 mL in a measuring cylinder. If its mass is 46.4 g, find its density in g/mL (g/cm³).
Step 1: Volume of metal = 58.2 − 50.0 = 8.2 mL (or cm³).
Step 2: Density = mass / volume = 46.4 g / 8.2 cm³ = 5.6585 ≈ 5.66 g/cm³.
Answer: ≈ 5.66 g/cm³.
Topic: Density and Volume (3)
3. A cylindrical rod of aluminium has length 10 cm and cross-sectional area 2 cm². If its density is 2.70 g/cm³, calculate its mass.
Step 1: Volume V = area × length = 2 cm² × 10 cm = 20 cm³.
Step 2: Mass = density × volume = 2.70 g/cm³ × 20 cm³ = 54 g.
Answer: 54 g.
Topic: Density and Volume (4)
4. A metal sphere of mass 28.35 g has density 8.96 g/cm³ (density of copper). Calculate the volume of the sphere in cm³.
Step 1: Volume = mass / density = 28.35 g / 8.96 g/cm³ = 3.16295 ≈ 3.163 cm³.
Answer: ≈ 3.163 cm³.
Topic: Density and Volume (5)
5. A rectangular block of metal measures 5.0 cm × 3.0 cm × 2.0 cm and has mass 90 g. Determine its density.
Step 1: Volume = 5.0 × 3.0 × 2.0 = 30.0 cm³.
Step 2: Density = mass / volume = 90 g / 30.0 cm³ = 3.0 g/cm³.
Answer: 3.0 g/cm³.
Topic: Density and Volume (6)
6. A 150 g sample of a metal occupies 18.75 cm³. Calculate the density and identify which common metal it might be close to (use approximate densities: Fe ≈ 7.87, Al ≈ 2.70, Cu ≈ 8.96 g/cm³).
Step 1: Density = mass / volume = 150 g / 18.75 cm³ = 8.0 g/cm³.
Step 2: Comparison: 8.0 g/cm³ is close to copper (8.96) and a bit higher than iron (7.87). It may be an alloy or approximate copper-like metal.
Answer: Density = 8.0 g/cm³ (approximately copper/iron range).
Topic: Density and Volume (7)
7. A piece of metal with density 7.2 g/cm³ weighs 180 g. Find its volume in cm³ and the dimensions of a cube with that volume (edge length ≈ ?).
Step 1: Volume = mass / density = 180 / 7.2 = 25 cm³.
Step 2: For a cube, edge³ = 25 → edge = ³√25 ≈ 2.924 cm.
Answer: Volume = 25 cm³; cube edge ≈ 2.92 cm.
Topic: Density and Volume (8)
8. Water displacement: A small irregular iron object when lowered into water raises the level from 120.0 mL to 123.5 mL. If the object weighs 28.05 g, calculate its density.
Step 1: Volume = 123.5 − 120.0 = 3.5 mL.
Step 2: Density = mass / volume = 28.05 / 3.5 = 8.0143 ≈ 8.01 g/cm³.
Answer: ≈ 8.01 g/cm³.
Topic: Percentage composition & Alloys (9)
9. An alloy of brass contains 70% copper by mass. If the total mass of the alloy is 250 g, find the mass of copper and zinc in it.
Step 1: Mass of copper = 70% of 250 = 0.70 × 250 = 175 g.
Step 2: Mass of zinc = total − copper = 250 − 175 = 75 g.
Answer: Copper = 175 g; Zinc = 75 g.
Topic: Percentage composition & Alloys (10)
10. A 200 g mixture of a metal and non-metal contains 15% non-metal by mass. Calculate masses of metal and non-metal.
Step 1: Mass of non-metal = 15% of 200 = 0.15 × 200 = 30 g.
Step 2: Mass of metal = 200 − 30 = 170 g.
Answer: Metal = 170 g; Non-metal = 30 g.
Topic: Percentage composition & Alloys (11)
11. A 120 g sample of an alloy contains 48 g of metal A. What percentage of A is present? (Give answer to one decimal place.)
Step 1: Percentage = (48 / 120) × 100% = 0.4 × 100% = 40.0%.
Answer: 40.0% of metal A.
Topic: Percentage composition & Alloys (12)
12. A metal sample loses 12% of its mass due to corrosion over several years. If initial mass was 500 g, find remaining mass.
Step 1: Mass lost = 12% of 500 = 0.12 × 500 = 60 g.
Step 2: Remaining mass = 500 − 60 = 440 g.
Answer: 440 g remains after corrosion.
Topic: Percentage composition & Alloys (13)
13. A 300 g sample contains two metals in ratio 2:1. Find masses of the two metals.
Step 1: Total parts = 2 + 1 = 3 parts.
Step 2: Mass of first metal = (2/3) × 300 = 200 g; second metal = (1/3) × 300 = 100 g.
Answer: 200 g and 100 g.
Topic: Practical measurement & conversions (14)
14. A student measures a metal block mass as 0.36 kg. Express its mass in grams and find volume if density is 9 g/cm³.
Step 1: Convert mass: 0.36 kg = 360 g.
Step 2: Volume = mass / density = 360 / 9 = 40 cm³.
Answer: Mass = 360 g; Volume = 40 cm³.
Topic: Practical measurement & conversions (15)
15. In an experiment, a piece of metal increased water level from 30.0 mL to 33.75 mL. If density is 2.70 g/cm³, calculate mass of the piece.
Step 1: Volume displaced = 33.75 − 30.0 = 3.75 cm³.
Step 2: Mass = density × volume = 2.70 × 3.75 = 10.125 g ≈ 10.13 g.
Answer: ≈ 10.13 g.
Topic: Practical measurement & conversions (16)
16. A 100 cm³ aluminium block has density 2.70 g/cm³. What is its mass in kg?
Step 1: Mass = density × volume = 2.70 × 100 = 270 g.
Step 2: Convert to kg: 270 g = 0.270 kg.
Answer: 0.270 kg.
Topic: Comparing metals & simple percentage (17)
17. Two equal-volume samples: iron (density 7.87 g/cm³) and aluminium (2.70 g/cm³). If each has volume 10 cm³, find their masses and which is heavier?
Step 1: Mass of iron = 7.87 × 10 = 78.7 g.
Step 2: Mass of aluminium = 2.70 × 10 = 27.0 g.
Step 3: Iron is heavier (78.7 g vs 27.0 g).
Answer: Iron = 78.7 g; Aluminium = 27.0 g; Iron is heavier.
Topic: Corrosion & Mass change (18)
18. A 250 g iron object corrodes and loses 6% mass. After cleaning, what mass remains? Also, what mass was lost?
Step 1: Mass lost = 6% of 250 = 0.06 × 250 = 15 g.
Step 2: Remaining mass = 250 − 15 = 235 g.
Answer: Remaining mass = 235 g; Mass lost = 15 g.
Topic: Uses & economics (19)
19. A metal sheet of copper (density 8.96 g/cm³) has volume 500 cm³. Calculate its mass in kilograms and approximate cost if copper costs ₹600 per kg.
Step 1: Mass = density × volume = 8.96 × 500 = 4480 g = 4.480 kg.
Step 2: Cost = 4.480 kg × ₹600/kg = ₹2688.
Answer: Mass = 4.480 kg; Cost ≈ ₹2,688.
Topic: Practical application & revision (20)
20. A student mixes 120 g of metal X with 80 g of metal Y to make an alloy. What percent (by mass) of metal X is in the alloy?
Step 1: Total mass = 120 + 80 = 200 g.
Step 2: Percentage of X = (120 / 200) × 100% = 60%.
Answer: Metal X is 60% by mass of the alloy.