Key MCQ Questions for Class 10 Maths Surface Area and Volume
FAQs on Surface Area and Volume MCQs for CBSE Class 10 Maths (2025-26)
1. What are the most frequently asked types of important questions from Chapter 13, Surface Area and Volume, in the CBSE Class 10 board exams for 2025-26?
Based on previous board exam trends, the most important questions from this chapter typically fall into three categories:
- Combination of Solids: Calculating the surface area or volume of a new shape formed by combining two or more basic solids (e.g., a tent made of a cylinder and a cone). These are often 3 or 5-mark questions.
- Conversion of Solids: Problems where one solid is melted and recast into another (e.g., a sphere melted to form multiple small cones). The key here is that the volume remains constant.
- Application-based Word Problems: Questions involving real-world scenarios like finding the capacity of a tank, the amount of water flowing through a pipe in a given time, or the cost of painting a composite object. These are often considered HOTS (Higher Order Thinking Skills) questions.
2. How are marks typically distributed for a 5-mark important question on the conversion of solids?
For a high-value 5-mark question, the marking scheme in the CBSE board exam is very specific to reward the correct methodology. A typical breakdown is:
- 1 Mark: For correctly identifying the principle that the volume of the original solid is equal to the volume of the recast solid(s) and writing the correct formulas.
- 1 Mark: For substituting the given values into the formulas accurately.
- 2 Marks: For performing the calculations correctly to find the unknown dimension or quantity.
- 1 Mark: For writing the final answer with the correct units (e.g., cm, m³, etc.).
Losing marks often happens in calculation errors or by forgetting the final units.
3. Which formulas are most crucial for solving 5-mark important questions in Surface Area and Volume?
To confidently solve 5-mark questions, you must have a strong command over the formulas for both surface area and volume of the basic shapes. The most critical formulas are:
- Cylinder: CSA (2πrh), TSA (2πr(r+h)), Volume (πr²h)
- Cone: CSA (πrl), TSA (πr(r+l)), Volume (1/3 πr²h)
- Sphere: Surface Area (4πr²), Volume (4/3 πr³)
- Hemisphere: CSA (2πr²), TSA (3πr²), Volume (2/3 πr³)
Remember to also know the relationship for a cone's slant height: l² = h² + r², as it is often needed to find a missing value.
4. When calculating the surface area of a combined solid, why don't we simply add the total surface areas (TSA) of the individual shapes?
This is a common conceptual error. You cannot simply add the TSAs because when two solids are joined, their joining surfaces are no longer exposed and are not part of the surface area of the new, combined object. For example, in a toy that is a cone mounted on a hemisphere, the base of the cone and the flat face of the hemisphere are joined together. Therefore, to find the total surface area of the toy, you must add the Curved Surface Area (CSA) of the cone and the Curved Surface Area (CSA) of the hemisphere only.
5. In questions where a solid is melted and recast, what is the key principle that ensures the correct answer, and what common mistakes should be avoided?
The single most important principle in problems involving the melting and recasting of solids is the conservation of volume. The volume of the material remains the same, regardless of the shape it takes. The most common mistake students make is incorrectly equating the surface areas instead of the volumes. Always remember: Shape changes, surface area changes, but volume remains constant.
6. How do important questions on a hollow cylinder differ from those on a solid cylinder?
Questions on hollow cylinders are more complex and are a frequent source of errors. The key differences are:
- Volume: For a solid cylinder, it's πr²h. For a hollow cylinder, you must calculate the volume of the material using the external (R) and internal (r) radii: π(R² - r²)h.
- Total Surface Area: For a solid cylinder, it's 2πr(r+h). For a hollow cylinder, the TSA includes the outer CSA (2πRh), the inner CSA (2πrh), and the area of the two circular rings at the top and bottom, which is 2π(R² - r²). Students often forget to include the area of these rings.
7. What type of question involving the combination of solids is expected in the board exam?
A highly expected question type involves calculating the surface area or capacity of a composite object. For the 2025-26 exam, prepare for questions based on real-life objects such as:
- A tent or building, shaped like a cylinder surmounted by a cone.
- An ice-cream cone, which is a cone topped with a hemisphere.
- A medical capsule, shaped like a cylinder with two hemispherical ends.
These questions test your ability to correctly identify the exposed surfaces and apply the right combination of CSA and TSA formulas.
8. What is a reliable step-by-step approach to solving complex word problems from this chapter for higher marks?
To tackle complex, high-value word problems effectively, follow this structured approach:
- Visualise and Draw: Read the problem carefully and draw a simple, neat diagram of the solid(s). This helps in understanding the geometry.
- List Given Data: Write down all the given values, such as radius, height, and slant height, with their units.
- Identify the Goal: Clearly determine whether you need to find the Volume, Curved Surface Area (CSA), or Total Surface Area (TSA).
- Select the Right Formula: Choose the correct formula(s) based on the shapes involved and the goal. For combined solids, be careful to add only the areas of the exposed surfaces.
- Calculate Methodically: Substitute the values and perform calculations step-by-step to minimise errors. Use π = 22/7 or 3.14 as specified in the question.
- State the Final Answer: Always conclude with a clear statement and the correct units (e.g., cm², m³). This step itself can carry a mark.
