Core
Surface Areas and Volumes: Core
Core
Surface Areas and Volumes (NCERT Ch. 11)
What you'll learn
- Find surface area and volume of cubes, cuboids, cylinders, cones, spheres.
- Use lateral vs total surface area correctly.
- Solve combination solids (ice-cream cone, tent, capsule).
- Convert units (cm³ to m³) and apply in word problems.
Key concepts
- Cuboid — TSA = 2(lb+bh+hl); volume = lbh.
- Cube — TSA = 6a²; volume = a³.
- Cylinder — CSA = 2πrh; TSA = 2πr(r+h); volume = πr²h.
- Cone — CSA = πrl; volume = (1/3)πr²h.
- Sphere — SA = 4πr²; volume = (4/3)πr³.
- Hemisphere — CSA = 2πr²; volume = (2/3)πr³.
- Composite solids — Add/subtract volumes carefully.
- NCERT — capacity and painting cost problems.
Worked example
Cylinder radius 7 cm, height 10 cm. Find volume.
V = πr²h = π·49·10 = 490π cm³ ≈ 1539.4 cm³
Common mistakes
- Skipping given-to-prove structure in geometry proofs.
- Using wrong congruence criterion (SSA is not valid).
- Forgetting units in length/angle statements.
Quick check
- State one NCERT result from Surface Areas and Volumes.
- Draw a neat diagram for a typical Surface Areas and Volumes problem.
Open the Practice tab for graded questions on Surface Areas and Volumes (NCERT Ch. 11).
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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