Class 10 Maths — Chapter 12: SURFACE AREAS AND VOLUMES
Chapter 12: SURFACE AREAS AND VOLUMES is a chapter in Class 10 Maths (NCERT), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 7 topics including Understanding Surface Area of Combined Solids, Surface Area of Cylinder-Hemisphere Combinations, Surface Area of Cone-Hemisphere Combinations. BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.
What you'll learn
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▸Understanding Surface Area of Combined SolidsCore conceptcombination of solidscomposite solidexposed surfacesurface area principle
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▸Surface Area of Cylinder-Hemisphere CombinationsCore conceptcylinderhemispherecapsuletankercurved surface area
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▸Surface Area of Cone-Hemisphere CombinationsCore conceptconehemispheresurmountedlattuslant height
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▸Surface Area of Solids with Surmounted ShapesCore conceptsurmountedcubehemispherebase arearemaining solid
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▸Surface Area of Solids with Depressions or CavitiesCore conceptdepressioncavityscooped outhollowed outinner surface
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▸Surface Area of Cylinder-Cone Combinationscylinderconetentrocketannulus
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▸Application in Real-World Problemsword problemsapplicationcost calculationcanvas areapainting
Chapter Summary
Recognize that the total surface area of a composite solid is the sum of the exposed surface areas of its constituent shapes, not the sum of their individual total surface areas.
Calculate the surface area of objects like a medicine capsule or a tanker, formed by a cylinder with one or two hemispheres attached to its ends by summing their respective curved surface areas.
Calculate the surface area of objects formed by joining a cone and a hemisphere along their circular bases, such as a toy top. This involves finding the individual Curved Surface Areas (CSAs) and adding them.
Calculate the surface area when one solid (e.g., a hemisphere) is placed on the face of another (e.g., a cube). This involves subtracting the covered base area and adding the new exposed surface area.
Determine the surface area of a solid after a shape (like a hemisphere or cone) has been scooped out. The internal surface area of the cavity is added to the remaining external area of the solid.
Calculate the surface area of composite objects like a tent or a rocket, formed by combining a cylinder and a cone. This may involve accounting for exposed base areas (annulus) if the radii differ.
Apply the principles of surface area calculation to solve multi-step word problems, such as finding the area to be painted or the cost of materials for a composite object.
Practice Questions from this Chapter
Tap "Get Solution" on any question to ask our AI tutor.
- Design a combined shape object? Get Solution →
- Estimate paint needed for a toy? Get Solution →
- Calculate water volume in a pool? Get Solution →
- According to the text, which four basic solids are mentioned as being familiar from Class IX? Get Solution →
- What is the shape of a test tube as described in the chapter? Get Solution →
- When calculating the volume of a new solid formed by joining two basic solids, how is the total volume determined? Get Solution →
- What does 'CSA' stand for in the context of this chapter? Get Solution →
- In Example 1, the playing top (lattu) is a combination of which two shapes? Get Solution →
Did you know?
- 💡 A sphere holds the most volume for its outside surface area.
- 💡 Ancient Greeks proved only five types of regular polyhedra exist.
- 💡 Honeybees use hexagonal cells, the most efficient shape for storing honey.
- 💡 Giant sequoia trees, the world's largest, grow in huge cylindrical shapes.
- 💡 All snowflakes have a six-sided, hexagonal symmetry, like a tiny prism.
Frequently Asked Questions
How many topics are covered in this chapter?
This chapter covers 7 key topics: Understanding Surface Area of Combined Solids, Surface Area of Cylinder-Hemisphere Combinations, Surface Area of Cone-Hemisphere Combinations, Surface Area of Solids with Surmounted Shapes, Surface Area of Solids with Depressions or Cavities, and more. The BrainWeave AI tutor explains each one with examples.
Is Chapter 12: SURFACE AREAS AND VOLUMES important for board exams?
Yes — Class 10 is a CBSE board exam year, and every NCERT chapter is part of the syllabus. Use BrainWeave's AI tutor to master this chapter, then practice with the auto-generated quizzes and mind maps.
Can I get NCERT solutions for this chapter in Hindi?
Yes. BrainWeave's AI tutor supports Hindi, English, and Hinglish for both voice and text chat. Just ask your question in your preferred language.
Is BrainWeave free for Class 10?
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