Important Mensuration Formulas for Area, Perimeter & Volume
The concept of Mensuration and Mensuration Formulas is essential in mathematics and helps in solving real-world and exam-level problems efficiently. It allows students to calculate area, perimeter, and volume of different shapes, which is fundamental for school exams and various competitive tests.
Understanding Mensuration and Mensuration Formulas
Mensuration refers to the branch of mathematics that deals with measuring the length, area, and volume of 2D and 3D geometric figures. Mensuration formulas are mathematical expressions used to calculate values such as area, perimeter, total surface area, lateral surface area, and volume for shapes like squares, rectangles, triangles, circles, cubes, cuboids, cylinders, cones, and spheres. This concept is widely used in geometry, competitive exams, engineering, and daily life problem-solving.
Key Terminologies in Mensuration
To use mensuration and mensuration formulas, it’s important to understand these common terms:
- Area: Surface covered by a closed figure (measured in square units).
- Perimeter: Total length around a figure’s boundary (measured in units).
- Volume: Space occupied by a 3D object (measured in cubic units).
- Curved Surface Area / Lateral Surface Area: Area of curved/lateral parts of solids.
- Total Surface Area: Sum of all surface areas of a solid.
Mensuration and Mensuration Formulas Table
Here is a complete table of mensuration formulas for key 2D and 3D shapes. These easy-to-read formulas will help you revise faster and are important for Class 8, Class 9, Class 10 and competitive exams.
Mensuration Formulas for 2D Shapes
| Shape | Area | Perimeter |
|---|---|---|
| Square | a² | 4a |
| Rectangle | l × b | 2(l + b) |
| Circle | πr² | 2πr |
| Triangle (Any) | ½ × base × height | Sum of all sides |
| Equilateral Triangle | (√3/4)a² | 3a |
| Parallelogram | base × height | 2(l + b) |
| Rhombus | ½ × d₁ × d₂ | 4 × side |
| Trapezium | ½ × h × (sum of parallel sides) | Sum of all sides |
Mensuration Formulas for 3D Shapes
| Shape | Volume | Curved/LSA | Total Surface Area (TSA) |
|---|---|---|---|
| Cube | a³ | 4a² | 6a² |
| Cuboid | l × b × h | 2h(l + b) | 2(lb + bh + hl) |
| Sphere | (4/3)πr³ | 4πr² | 4πr² |
| Hemisphere | (2/3)πr³ | 2πr² | 3πr² |
| Cylinder | πr²h | 2πrh | 2πr(h + r) |
| Cone | (1/3)πr²h | πrl | πr(r + l) |
These mensuration formulas are vital for board exams, competitive papers, and everyday mathematics.
Mensuration Formulas PDF Download
Students can quickly access revision notes by downloading mensuration and mensuration formulas PDF. These can be printed for last-minute revision or used on mobile devices.
Example PDFs to download from trusted sources:
Worked Example – Solving Mensuration Problems
Let’s see how mensuration formulas are used in real exam questions:
1. Find the area and perimeter of a square with side 8 cm.2. Calculate the volume of a cylinder with radius 3 cm, height 7 cm.
3. The area of a rhombus with diagonals 12 cm and 16 cm?
Practice Problems
- Find the total surface area of a cube of side 5 cm.
- If the radius of a circle is 14 cm, find its area and circumference.
- Calculate the volume of a cone with height 10 cm and base radius 4 cm.
- The length, breadth, and height of a cuboid are 4 cm, 5 cm, and 6 cm. Find its volume.
Common Mistakes to Avoid
- Mixing up area and perimeter formulas for similar shapes.
- Using wrong units (confusing cm, cm², and cm³).
- Forgetting to use the correct version of π (3.14 or 22/7) as needed.
- Not checking if question is about 2D or 3D shape before applying formulas.
Real-World Applications of Mensuration Formulas
Mensuration is widely used for calculating paint needed for walls, fabric for stitching, storage capacities, and even in construction/architecture. Knowing mensuration and mensuration formulas helps students and professionals solve practical, day-to-day problems efficiently. Vedantu provides clear explanations and resources to connect these concepts to real life.
Class-wise Mensuration Formulas
For thorough revision, see class-specific formula pages:
- Mensuration for Class 8
- Mensuration Formulas for Class 10
- Maths Formulas for Class 11
- Maths Formulas for Class 12
Further Resources and Related Vedantu Pages
Explore more detailed concepts and examples here:
- Area of Isosceles Triangle
- Volume of Cube, Cuboid, and Cylinder
- Perimeter of a Polygon
- Surface Area of Cone
- Areas of Parallelograms and Triangles
- Area of a Circle
- Surface Area of a Cylinder
- Area and Perimeter
- Surface Area and Volume
We explored the idea of mensuration and mensuration formulas, how they are used in maths, and their daily relevance. For step-by-step learning, worked examples, and more practice, rely on Vedantu to strengthen your foundation in mensuration for every class and exam need.
FAQs on All Mensuration Formulas with Examples and Quick Revision
1. What are the formulas of mensuration?
Mensuration formulas help calculate the area, perimeter, volume, curved surface area, lateral surface area, and total surface area of various 2D and 3D geometric shapes. Common formulas include those for squares, rectangles, triangles, circles, cubes, cylinders, cones, spheres, and hemispheres. These formulas are essential for solving problems in math board exams and competitive exams.
2. What is mensuration in maths?
Mensuration is a branch of mathematics that involves measuring the length, area, perimeter, and volume of various geometric shapes. It covers both 2D shapes like squares and circles, where we calculate area and perimeter, and 3D solids like cubes and cylinders, where volume and surface areas are calculated.
3. Where can I download mensuration formulas PDF?
You can download comprehensive and free Mensuration Formulas PDFs from trusted educational websites such as Vedantu and Career Power. These PDFs contain all important formulas for both 2D and 3D shapes, class-wise sections, and are designed for quick exam revision and practice. Example links include official Vedantu formula PDFs and other reputable sources.
4. Which formulas are important for Class 10/12 board exams?
For Class 10 and Class 12 board exams, focus on formulas related to all common 2D figures such as triangle types, circle, quadrilaterals, and trapeziums, as well as important 3D solids like cuboids, cylinders, cones, spheres, and hemispheres. Key formulas include area, perimeter, volume, curved surface area (CSA), and total surface area (TSA). Knowing application-based examples helps greatly in exams.
5. Can you give examples using mensuration formulas?
Yes, solved examples clarify practical application of mensuration formulas. For instance:
- To find the area of a square: use Area = a² where a is side length.
- Calculate the circumference of a circle using Circumference = 2πr.
- Volume of a cylinder is V = πr²h, where r is radius and h is height.
Step-by-step solutions help in understanding how to substitute values and perform calculations correctly.
6. What is the difference between area and volume in mensuration?
The area refers to the measurement of the surface enclosed by a 2D shape and is expressed in square units (e.g., cm²). The volume measures the space occupied by a 3D object and is expressed in cubic units (e.g., cm³). While area deals with flat surfaces, volume involves the capacity inside a solid shape.
7. Why do students confuse area and perimeter formulas for different shapes?
Students often confuse area and perimeter formulas because both involve calculating properties of shapes but measure different things—area measures surface and perimeter measures boundary length. Additionally, misuse of formulas across similar shapes can cause mistakes. Careful learning with visual aids and repeated practice differentiates these concepts clearly.
8. How can class-specific mensuration formulas be quickly revised?
Quick revision of class-specific mensuration formulas is effective through:
1. Using tabular cheat sheets that list formulas by class syllabus.
2. Downloading and reviewing PDF formula sheets tailored to Class 8, 9, 10, and 12.
3. Practicing solved examples relevant to class exam patterns.
4. Using accordion or collapsible FAQs for easy mobile reading.
This strategy ensures focused and fast recall of formulas during board or competitive exams.
9. Why are 3D mensuration formulas often forgotten in exams?
3D mensuration formulas are often forgotten because:
- They involve more complex calculations than 2D formulas.
- Students sometimes lack practical visualization of 3D solids.
- Insufficient practice on volume and surface area questions.
To overcome this, regular practice with real-life problems, use of model diagrams, and stepwise problem-solving enhances retention and confidence.
10. Which is best for learning: formula chart or solved example?
Both formula charts and solved examples serve different but complementary learning purposes:
- Formula charts provide a quick reference and aid memorization of key mensuration formulas.
- Solved examples demonstrate how to apply these formulas practically, improving problem-solving skills.
For effective learning, a combination of both is recommended, starting with formula familiarization and then practicing multiple examples.
11. Why do competitive exams test tricky mensuration applications?
Competitive exams often test tricky mensuration problems to assess a student's ability to:
- Understand and apply multiple formulas in combination.
- Analyze geometrical reasoning beyond straightforward calculations.
- Manage time and accuracy under exam conditions.
Such questions require deeper conceptual clarity and practice, which is why focused revision and problem-solving preparation are essential for aspirants.
