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Essential Study Materials for Surface Areas and Volumes Class 10 Maths 2025-26
Mastering Surface Areas & Volumes for Class 10 Maths: CBSE 2025-26 Guide
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FAQs on Mastering Surface Areas & Volumes for Class 10 Maths: CBSE 2025-26 Guide
1. What types of questions are considered most important from Chapter 13, Surface Areas and Volumes, for the CBSE Class 10 Board Exam 2025-26?
For the Class 10 board exams, the most important questions from this chapter focus on practical applications and combinations of solids. Key types include:
- Surface Area of Combined Solids: Calculating the total surface area of objects made from two or more basic shapes, like a cone mounted on a cylinder or a hemisphere on a cube.
- Volume of Combined Solids: Finding the capacity or volume of composite solids.
- Conversion of Solids: Problems where one solid is melted or reshaped into another, requiring you to equate their volumes.
- Case-Study Questions: Multi-part, application-based problems, often carrying 4 or 5 marks, that test your ability to deconstruct a real-world object into geometric shapes.
2. How do I decide which surface areas to add when calculating the Total Surface Area (TSA) of a combined solid?
This is a critical concept that is frequently tested. When two solids are joined, the surfaces where they meet are no longer exposed and must be excluded from the calculation. You should only add the areas of the visible or exposed surfaces. For example, to find the TSA of a toy shaped like a cone on top of a hemisphere, you would add the Curved Surface Area (CSA) of the cone and the CSA of the hemisphere. The circular base of the cone and the top of the hemisphere are not included as they are joined together.
3. What is the expected marks distribution for important questions from Surface Areas and Volumes?
Based on previous board exam trends, you can typically expect a mix of questions from this chapter:
- 1-mark questions (MCQs): These test direct formula knowledge or a basic conceptual understanding.
- 2 or 3-mark questions: These usually involve a straightforward calculation of volume or surface area for a combined solid with two shapes.
- 4 or 5-mark questions: These are often long-answer or case-study problems involving complex solid conversions or combinations of three or more shapes, requiring detailed step-by-step calculations.
4. In questions involving the conversion of a solid (e.g., melting a sphere to form a wire), what is the core principle used for solving?
The fundamental principle is the conservation of volume. When a solid is melted, recast, or reshaped, its form and surface area change, but the amount of material does not. Therefore, the volume of the original solid is always equal to the volume of the new solid. You must set up an equation where Volume (Shape 1) = Volume (Shape 2) to solve for any unknown dimension like radius, height, or length.
5. What are the most common mistakes to avoid in Surface Areas and Volumes to score full marks?
Students often lose marks due to simple errors. Pay close attention to avoid these:
- Calculation Errors: Be meticulous with your arithmetic, especially when using π (use 22/7 or 3.14 as specified in the question).
- Formula Confusion: Do not mix up formulas for volume and surface area, or the CSA and TSA of a shape.
- Unit Inconsistency: Ensure all dimensions (radius, height, etc.) are in the same unit before you begin calculations.
- Incorrectly Adding TSAs: A very common error in combined solids is adding the individual TSAs. Remember to only sum up the exposed surface areas.
6. Can two solid shapes have the same volume but different surface areas? How is this concept tested in exams?
Yes, absolutely. For a given volume, different shapes will have different surface areas. A sphere, for instance, has the minimum possible surface area for its volume compared to any other shape. This is a key concept for High Order Thinking Skills (HOTS) questions. An exam question might ask which container shape (e.g., cylindrical vs. cubical) with the same capacity would be cheaper to manufacture. This is an indirect way of asking which shape has a smaller surface area for the same volume, as less material would be needed.
7. Which formulas are essential for solving all important questions from this chapter?
To excel in this chapter, you must memorise the following formulas as per the NCERT syllabus for 2025-26:
- Cylinder: CSA = 2πrh, TSA = 2πr(r + h), Volume = πr²h
- Cone: CSA = πrl, TSA = πr(l + r), Volume = (1/3)πr²h
- Sphere: Surface Area = 4πr², Volume = (4/3)πr³
- Hemisphere: CSA = 2πr², TSA = 3πr², Volume = (2/3)πr³
- Cuboid: TSA = 2(lb + bh + hl), Volume = lbh
- Cube: TSA = 6a², Volume = a³
8. What is the best strategy to solve a 5-mark case-study question from this chapter in the board exam?
To confidently tackle a 5-mark case study, follow a structured approach:
- Draw a Diagram: First, read the scenario and sketch a rough, labelled diagram of the composite object. This helps in visualising the components.
- Break Down the Shape: Clearly identify the individual geometric solids that form the object (e.g., a cylinder with hemispherical ends).
- Identify the Goal: Determine precisely what needs to be calculated. Is it the volume (capacity), the area to be painted (surface area), or some other dimension?
- Select and Apply Formulas: Write down the correct formulas for the required property of each component shape and combine them logically. For instance, Volume(Capsule) = Volume(Cylinder) + 2 × Volume(Hemisphere).
- Show Step-by-Step Work: Present your calculations clearly. This ensures you can receive partial credit even if there is a final calculation error.
