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Surface Areas and Volumes
This chapter helps students work with the surface area and volume of common solids such as cylinders, cones, spheres, and hemispheres. The key exam habit is to identify the correct part of the solid first: curved surface, total surface, or full volume. Many mistakes happen when students mix radius, height, and slant height, so every formula must be used with care and proper units. The chapter also includes recasting and combination of solids, which are very important in CBSE Class 10 questions. In such problems, volume is usually conserved when material is reshaped, while surface area problems require attention to exposed parts only. A strong grip on formulas, diagrams, and common mistakes can turn this chapter into a scoring one.
Difficulty
Medium
Study time
96-120 min
Plan by time
Pick the window that matches what you have right now.
If you have 15 min
Last-pass revision
Skim the Quick Revision table — definitions, formulas, and the traps board examiners reuse.
Open Quick RevisionIf you have 45 min
Targeted practice
Read the high-priority concepts, then take the chapter MCQ quiz to find weak spots.
Start MCQ QuizIf you have 96 min
First full pass
Walk every concept in chapter order, then revise and quiz. Best for the first time you study this chapter.
Open Key ConceptsChapter Learning Map
Start with one of the buckets below, then open the full map when you want the complete concept roadmap.
Key Concepts
Concepts grouped the way the chapter is taught — open the bucket that matches what you want to revise.
Core Concepts
high priorityOpen the chapter concepts in a clean revision order.
Curved surface area of a cylinder
The curved surface area of a cylinder is the area of only the side surface, excluding both circular bases.
Total surface area of a cylinder
The total surface area of a cylinder is the area of its curved surface plus the areas of both circular bases.
Volume of a cylinder
The volume of a cylinder is the amount of space enclosed inside it.
Curved surface area of a cone
The curved surface area of a cone is the area of its sloping side, excluding the circular base.
Total surface area of a cone
The total surface area of a cone is the area of its curved surface plus the area of its circular base.
Volume of a cone
The volume of a cone is one-third of the volume of a cylinder having the same base radius and height.
Surface area of a sphere
The surface area of a sphere is the total area of its outer curved surface.
Volume of a sphere
The volume of a sphere is the amount of space enclosed inside it.
Surface area of a hemisphere
The surface area of a hemisphere is the curved surface plus the circular base when the whole outer surface is asked for.
Volume of a hemisphere
The volume of a hemisphere is half the volume of a sphere with the same radius.
Conversion of one solid into another
When one solid is melted, recast, or reshaped into another solid without wastage, the volume of material remains the same.
Combination of solids
A combination of solids is a shape formed by joining two or more simple solids together.
Exam Intelligence
Use this section to decide what deserves the most revision time.
High Probability Topics
- Curved surface area of a cylinder
- Total surface area of a cylinder
- Volume of a cylinder
- Curved surface area of a cone
- Total surface area of a cone
- Volume of a cone
- Surface area of a sphere
- Volume of a sphere
Common Traps
- Using total surface area when only curved surface area is asked.
- Forgetting to square or cube the radius in volume formulas.
- Using slant height instead of perpendicular height in cone volume.
- Counting hidden joined faces in composite solids.
- Mixing surface area with volume in recasting questions.
- Using the wrong hemisphere formula when the base is included.
Likely Question Types
- MCQ: concept checks, applications, and common mistakes
- Very short answer: definitions, formulas, or conditions
- Short answer: worked method, example, or reason-based explanation
- Case-based: chapter scenario with concept-linked subparts
Quick Revision
Concept, formula or equation to remember, and the trap that loses marks — in one scannable view.
- Cylinder formulas depend on radius and height.
- Cone formulas use slant height for curved area and perpendicular height for volume.
- Sphere formulas depend only on radius.
- Hemisphere area changes when the base is included.
- Recasting problems use equal volumes.
- Composite solid problems need careful addition and hidden-surface checking.
- Curved surface area of a cylinder: The curved surface area of a cylinder is the area of only the side surface, excluding both circular bases.
- Total surface area of a cylinder: The total surface area of a cylinder is the area of its curved surface plus the areas of both circular bases.
Practice
Use short concept checks first, then move into the full chapter test.
Free Chapter MCQ Quiz
Try a 15-question quiz from this chapter. Get instant score and unlock concept-wise analytics.
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