Page 1: Introduction
This chapter deals with surface area and volume of 3D solids: cuboid, cube, cylinder, cone, sphere, and hemisphere.
We learn formulas, applications, and problems involving conversion of solids (melting/recording).
Important for board exams and real-life measurements.
Page 2: Cuboid
Total Surface Area = 2(lb + bh + hl)
Volume = l × b × h
Page 3: Cube
Total Surface Area = 6a²
Volume = a³
All faces square, a = side.
Page 4: Right Circular Cylinder
Total Surface Area = 2πr(h + r)
Volume = πr²h
Page 5: Right Circular Cone
Curved Surface Area = πrl
Total Surface Area = πr(l + r)
Volume = (1/3)πr²h
Page 6: Sphere
Volume = (4/3)πr³
Page 7: Hemisphere
Total Surface Area = 3πr²
Volume = (2/3)πr³
Solid hemisphere includes base.
Page 8: Formula Summary Table
All solids with CSA, TSA, Volume formulas listed clearly.
Page 9: Conversion of Solids
When one solid is melted and recast into another, volume remains same.
Use Volume1 = Volume2 to find unknown dimension.
Page 10: Example - Melting Problems
a³ = (4/3)πr³ → r = ...
Page 11: Key Points
- Use π = 22/7 or 3.14 as per question
- Slant height crucial for cone
- Hemisphere TSA includes base
- Volume conserved in melting
Page 12: Practice Questions - Easy (1-10)
- TSA of cube side 5 cm.
- Volume of cylinder r=7, h=10.
- Slant height of cone r=5, h=12.
- CSA of sphere r=14.
- Volume of hemisphere r=3.
- TSA of cuboid 10×8×6.
- Find height of cylinder volume 308 cm³, r=7.
- CSA of cone l=25, r=7.
- Volume of cube side 9 cm.
- Surface area of sphere volume 36π.
Page 13: Practice Questions - Medium (11-20)
- Cylinder melted into cone, find height.
- Sphere recast into cylinder, find r/h.
- Find TSA of hemisphere.
- Cone volume given, find slant height.
- Cuboid melted into sphere, find radius.
- Compare volumes of cylinder and cone same base/height.
- Find cost of painting cylinder.
- Hemisphere volume, find r.
- Combined solid: cylinder + hemisphere.
- Find slant height given CSA.
Page 14: Practice Questions - Hard (21-30)
- Complex melting: cube → cylinder → cone.
- Solid with hollow hemisphere.
- Maximum volume sphere from cylinder.
- Water level rise problems.
- Find dimensions using both SA and volume.
- Combined cone + cylinder volume.
- Material used for hollow cylinder.
- Advanced conversion with ratio.
- Real-life bucket problem.
- Optimisation type question.
Page 15: NCERT Exercise Types
Direct formula application, melting problems.
Page 16: Formula Table
All formulas in tabular format for quick revision.
Page 17: Common Mistakes to Avoid
- Forgetting base in hemisphere TSA
- Wrong slant height calculation
- Mixing CSA and TSA
- Using wrong value of π
- Forgetting volume conservation
Page 18: Previous Year Board Questions
Melting/recording, combined solids, cost problems.
Page 19: Exam Strategy Tips
- Memorise all formulas exactly
- Write units clearly
- Show step-by-step calculation
- Check if hollow or solid
- Use π value as given
Page 20: Quick Revision Formula Sheet
All important formulas listed with diagrams description.
Page 21: Melting Problems Tips
Volume same → set volumes equal → solve.
Page 22: Final Motivation
You've completed the 27-page Surface Areas and Volumes guide!
This chapter is scoring if formulas memorised.
Practice melting problems daily.
You're almost done with Class 9 Maths 🦖
Page 23: Extra Examples
More solved problems.
Page 24: Combined Solids
How to handle cylinder + cone/hemisphere.
Page 25: Real-Life Applications
Tanks, buckets, spheres, etc.
Page 26: Formula Memorisation Trick
Mnemonics and grouping.
Page 27: Thank You & Copyright
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