Mensuration Formulas Table for Class 10: Area, Surface Area & Volume Explained
The concept of Mensuration formulas class 10 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. For CBSE and ICSE students, mastering mensuration helps solve questions on areas, perimeters, volumes, and surface areas of different shapes. Learning these formulas is vital for quick calculations in board exams, competitive tests, and even practical daily uses like planning, building, or crafting.
What Is Mensuration Formulas Class 10?
A Mensuration formula is a mathematical equation used to calculate measurements like area, perimeter, volume, and surface area of geometrical shapes. In class 10 Maths, these formulas are applied to 2D and 3D shapes such as rectangles, triangles, circles, cubes, cuboids, cylinders, cones, spheres, and hemispheres. You’ll find this concept applied in areas such as probability, geometry, and real-life measurement problems.
Key Formula for Mensuration Formulas Class 10
Here’s the standard formula: Each shape has its own formula. For example, area of rectangle: \( \text{Area} = l \times b \); volume of cube: \( V = a^3 \); curved surface area of cylinder: \( 2\pi r h \); area of circle: \( \pi r^2 \). See the complete mensuration formulas class 10 chart below.
| Shape | Area | Perimeter / Circumference | Volume | Surface Area (TSA/CSA/LSA) |
|---|---|---|---|---|
| Square | \( a^2 \) | \( 4a \) | – | – |
| Rectangle | \( l \times b \) | \( 2(l + b) \) | – | – |
| Triangle | \( \frac{1}{2} \times b \times h \) | Sum of all sides | – | – |
| Circle | \( \pi r^2 \) | \( 2\pi r \) | – | – |
| Parallelogram | \( b \times h \) | \( 2(a + b) \) | – | – |
| Trapezium | \( \frac{1}{2} (a + b) h \) | Sum of all sides | – | – |
| Cube | – | – | \( a^3 \) | TSA: \( 6a^2 \), LSA: \( 4a^2 \) |
| Cuboid | – | – | \( l \times b \times h \) | TSA: \( 2(lb + bh + hl) \), LSA: \( 2h(l + b) \) |
| Cylinder | – | – | \( \pi r^2 h \) | CSA: \( 2\pi r h \), TSA: \( 2\pi r(h + r) \) |
| Cone | – | – | \( \frac{1}{3}\pi r^2 h \) | CSA: \( \pi r l \), TSA: \( \pi r (l + r) \) |
| Sphere | – | – | \( \frac{4}{3}\pi r^3 \) | TSA: \( 4\pi r^2 \) |
| Hemisphere | – | – | \( \frac{2}{3}\pi r^3 \) | CSA: \( 2\pi r^2 \), TSA: \( 3\pi r^2 \) |
Cross-Disciplinary Usage
Mensuration formulas class 10 are not only useful in Maths but also play an important role in Physics (e.g., calculating volumes and densities), Computer Science (like area calculations in graphics), and logical reasoning tasks in daily life. Students preparing for exams like JEE or NEET will see its relevance in geometry, vectors, and measurement-based questions.
Step-by-Step Illustration
Let’s solve a typical exam problem using mensuration formulas class 10.
1. Question: Find the total surface area (TSA) of a cuboid with length = 6 cm, breadth = 4 cm, height = 3 cm.2. Write formula: TSA = \( 2(lb + bh + hl) \)
3. Substitute values: \( 2[(6 \times 4) + (4 \times 3) + (3 \times 6)] = 2[24 + 12 + 18] = 2[54] = 108 \) cm²
4. Final Answer: TSA = 108 cm²
Speed Trick or Vedic Shortcut
Here’s a quick shortcut for remembering mensuration formulas class 10: For 3D shapes, the pattern is usually “area = sum of all faces”, “volume = base area × height", “curved area = curved part only". Use unit cubes or draw nets to visualize. Also, for a cube, every formula involves ‘a’ to the power 2 or 3, which is easy to spot!
Example Trick: To remember the TSA of a cylinder: Just add area of two bases and the lateral curved area. TSA = \( 2\pi r h + 2\pi r^2 = 2\pi r (h + r) \).
Tricks like these help in board exams. Vedantu’s expert teachers also share PDFs and infographics for last-moment revision.
Try These Yourself
- Find the area and perimeter of a rectangle with sides 12 cm and 5 cm.
- Calculate the volume and total surface area of a cube of side 7 cm.
- What is the curved surface area of a cylinder with radius 3 cm and height 10 cm?
- Use the formula for a cone to get its volume for r = 4 cm, h = 9 cm.
Frequent Errors and Misunderstandings
- Confusing LSA (lateral) and TSA (total surface area).
- Mixing up ‘r’ (radius) and ‘h’ (height) in cylindrical/conical formulas.
- Forgetting to use the correct units (cm² for area, cm³ for volume).
- Applying 2D formulas to 3D shapes.
Relation to Other Concepts
The idea of mensuration formulas class 10 connects closely with topics such as area and perimeter and surface area and volume. Mastering these formulas helps build a strong base for higher classes, competitive exams, and real-world applications in architecture and design.
Classroom Tip
A quick way to remember mensuration formulas class 10 is to make a formula chart for your wall or notebook. Always write units next to your answers. Vedantu’s teachers often use diagrams and nets to make these concepts easier during live sessions, and you can also download handy PDF sheets from trusted study portals.
We explored mensuration formulas class 10—from definition, formula, examples, mistakes, and connections to other subjects. Continue practicing with Vedantu to become confident in solving problems using this concept and to prepare effectively for your exams!
Further Learning Resources
- Surface Area and Volume – Class 10 solutions and extra examples
- Area and Perimeter – In-depth concepts and solved sums for all boards
- Area of a Circle – Complete guide to circle problems with visuals and tricks
- Volume and Capacity – Learn more about 3D shapes, volume tricks, and exam questions
FAQs on Class 10 Mensuration Formulas: Complete Guide for Exams
1. What are the main mensuration formulas for Class 10?
The most important mensuration formulas for Class 10 cover the area and perimeter of 2D shapes like circles, squares, rectangles, and triangles, along with the volume and surface area of 3D shapes such as cubes, cuboids, cylinders, cones, and spheres. A comprehensive formula chart is essential for quick revision.
2. How do I memorize all area and volume formulas for board exams?
Effective memorization strategies include creating a formula chart, using visual aids like diagrams, employing mnemonic devices or memory tricks, and practicing solving numerous word problems. Regularly reviewing the formulas and using flashcards can significantly aid retention. Focus on understanding the derivations of formulas to enhance long-term memory.
3. What is the difference between 2D and 3D mensuration?
2D mensuration involves calculating the area and perimeter of flat shapes like circles and squares. 3D mensuration focuses on calculating the volume and surface area of solid objects like cubes and spheres. Essentially, 2D deals with two dimensions (length and width), while 3D includes a third dimension (height or depth).
4. Can I download a printable formula chart for Class 10 mensuration?
Yes, many resources online provide printable formula charts for Class 10 mensuration. Look for reputable educational websites offering downloadable PDFs or worksheets. These charts are extremely helpful for quick revision and exam preparation.
5. Where can I find solved word problems on mensuration for Class 10?
Numerous textbooks, online resources, and educational websites offer solved examples and practice problems on Class 10 mensuration. Vedantu provides a wealth of resources, including solved examples and practice exercises to improve your problem-solving skills.
6. Why is π (pi) used in so many area and volume formulas?
π (pi) represents the ratio of a circle's circumference to its diameter. It's a constant approximately equal to 3.14159. Because circles and parts of circles (like sectors and segments) are fundamental components of many shapes, π appears frequently in mensuration formulas involving curved surfaces and volumes.
7. Are mensuration formulas different in ICSE and CBSE Class 10?
The core mensuration formulas are largely the same in both CBSE and ICSE Class 10 syllabi. However, the complexity of problems and the emphasis on specific topics may vary slightly. It's always best to refer to the specific syllabus for your board.
8. When is it better to use the curved surface area, and when the total surface area?
Use curved surface area when dealing with only the curved portion of a 3D shape, such as the lateral surface of a cylinder or cone. Use total surface area when you need the entire surface area, including the bases or flat surfaces, of the object.
9. How do mensuration mistakes most commonly happen in multi-step problems?
Common mistakes in multi-step mensuration problems include incorrect unit conversions, inaccurate formula application, calculation errors (especially with decimals and fractions), and overlooking crucial details in the problem statement. Carefully reviewing each step and double-checking calculations is crucial.
10. Can mensuration formulas help solve real-world design and architecture problems?
Absolutely! Mensuration is fundamental in various fields, including architecture, engineering, and interior design. Architects and engineers use mensuration principles to calculate material quantities, determine volumes of spaces, and design structures with precise dimensions. Understanding mensuration is critical for practical applications.
11. What are some common units used in mensuration?
Common units used in mensuration include meters (m) and centimeters (cm) for length, square meters (m²) and square centimeters (cm²) for area, and cubic meters (m³), cubic centimeters (cm³), and liters (L) for volume.
12. How can I improve my speed in solving mensuration problems?
Practicing regularly is key. Focus on mastering the formulas, understanding their derivations, and solving a variety of problems. Develop efficient calculation techniques, use calculators effectively where permitted, and learn to recognize patterns in problem types to streamline your approach.
