Page 1: Introduction
Chapter deals with surface area and volume of 3D solids and combinations.
Solids: cuboid, cube, cylinder, cone, sphere, hemisphere, frustum.
Conversion problems (melting/recording) very common.
Page 2: Cuboid and Cube
Volume = lbh
Cube TSA = 6a², Volume = a³
Page 3: Cylinder
TSA = 2πr(h + r)
Volume = πr²h
Page 4: Cone
CSA = πrl
TSA = πr(l + r)
Volume = (1/3)πr²h
Page 5: Sphere and Hemisphere
Hemisphere: CSA = 2πr², TSA = 3πr², Volume = (2/3)πr³
Page 6: Frustum of Cone
CSA = π(R + r)l
TSA = π(R + r)l + π(R² + r²)
Volume = (1/3)πh(R² + Rr + r²)
Page 7: Combination of Solids
Add/subtract volumes and surfaces accordingly.
Common: cone on cylinder, hemisphere on cube.
Page 8: Conversion of Solid
Volume remains same in melting/recording.
Use Volume₁ = Volume₂ to find unknown dimension.
Page 9: Key Formulas Table
| Solid | TSA/CSA | Volume |
|---|---|---|
| Cuboid | 2(lb+bh+hl) | lbh |
| Cylinder | 2πr(h+r) | πr²h |
| Cone | πr(l+r) | (1/3)πr²h |
| Sphere | 4πr² | (4/3)πr³ |
| Hemisphere | 3πr² | (2/3)πr³ |
Page 10: Practice Questions - Easy (1-10)
- TSA of cube side 5 cm.
- Volume of cylinder r=7, h=10.
- Slant height cone r=5, h=12.
- CSA sphere r=14.
- Volume hemisphere r=3.
- TSA cuboid 10×8×6.
- Find height cylinder volume 308 cm³, r=7.
- CSA cone l=25, r=7.
- Volume cube side 9 cm.
- Surface area sphere volume 36π/ something.
Page 11: Practice Questions - Medium (11-20)
- Cylinder melted into cone, find height.
- Sphere recast into cylinder, find r/h.
- TSA of solid hemisphere.
- Frustum volume given R,r,h.
- Cuboid melted into sphere, find radius.
- Combined cylinder + hemisphere volume.
- Cost of painting cylinder.
- Hollow hemisphere material.
- Frustum CSA numerical.
- Cone on cylinder total SA.
Page 12: Practice Questions - Hard (21-30)
- Complex conversion chain.
- Frustum from cone cutting.
- Water level rise in container.
- Maximum volume sphere from cylinder.
- Hollow cylinder material.
- Combined cone + hemisphere + cylinder.
- Bucket (frustum) volume.
- Board level conversion.
- Solid with cavity.
- Optimisation type.
Page 13: Formula Table
All solids with CSA, TSA, Volume.
Page 14: Common Mistakes
- Forgetting base in hemisphere TSA
- Wrong slant height
- Mixing CSA and TSA
- Volume not conserved in conversion
- Frustum formula error
Page 15: Previous Year Questions
Conversion, combined solids, frustum, cost.
Page 16: Exam Tips
- Memorise all formulas
- Identify solid type
- Volume same in conversion
- Draw diagram for combined
- Use π value given
Page 17: Quick Revision Sheet
All formulas, units.
Page 18: Final Motivation
Chapter 13 complete! Mensuration is scoring with formulas memorised.
Practice conversion and combined.
Class 10 Maths unstoppable 🦖
Page 19: Extra Numericals
More solved problems.
Page 20: Frustum Special
Detailed formula and example.
Page 21: Conversion Tips
Volume equality method.
Page 22: Combined Solids
How to handle.
Page 23: Board Pattern
Common questions.
Page 24: Extra Practice
More questions.
Page 25: Real-Life Applications
Tanks, buckets, spheres.
Page 26: Formula Memorisation
Grouping and tricks.
Page 27: Thank You & Copyright
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