What is Mensuration Class 8: Complete Guide for NCERT Students
By ConceptScroll Team · Published on 19 June 2026 · 4 min read
What is Mensuration Class 8? Mensuration is a branch of mathematics that deals with measuring lengths, areas, and volumes of different geometric shapes. This chapter is important for Class 8 NCERT students to understand how to calculate perimeter, surface area, and volume of 2D and 3D figures.
Introduction to Mensuration in Class 8 Mathematics
Mensuration is a fundamental chapter in Class 8 NCERT Mathematics that focuses on calculating the size and dimensions of different shapes. It helps students learn how to find:
- Perimeter (length around 2D shapes)
- Area (surface covered by 2D shapes)
- Surface area (total area covering 3D solids)
- Volume (space occupied by 3D solids)
This chapter builds on earlier concepts from Classes 6 and 7 and introduces more complex solids and formulas. Understanding mensuration improves problem-solving skills and prepares students for higher classes.
Basic Formulas for Perimeter and Area of Plane Figures
In mensuration, plane figures are flat shapes like squares, rectangles, triangles, and circles. Here are the basic formulas:
| Shape | Perimeter Formula | Area Formula |
|---|---|---|
| Square | $P = 4a$ | $A = a^2$ |
| Rectangle | $P = 2(l + b)$ | $A = l imes b$ |
| Triangle | $P = a + b + c$ | $A = \frac{1}{2} \times base \times height$ |
| Circle | $P = 2\pi r$ (Circumference) | $A = \pi r^2$ |
Example: Find the area of a rectangle with length 8 cm and breadth 5 cm.
$$ A = l \times b = 8 \times 5 = 40 \text{ cm}^2 $$
Want to test yourself on Mensuration? Try our free quiz →
Surface Area of Common 3D Solids
Surface area is the total area covering the outer surface of a 3D solid. Common solids studied in Class 8 include cubes, cuboids, cylinders, cones, and spheres.
- Cube: $SA = 6a^2$
- Cuboid: $SA = 2(lb + bh + hl)$
- Cylinder: $SA = 2\pi r(h + r)$
- Cone: $SA = \pi r(l + r)$ where $l$ is slant height
- Sphere: $SA = 4\pi r^2$
Example: Calculate the surface area of a cube with side 4 cm.
$$ SA = 6 \times 4^2 = 6 \times 16 = 96 \text{ cm}^2 $$
Volume of 3D Solids in Mensuration Class 8
Volume measures the space occupied by a 3D object. The formulas for common solids are:
- Cube: $V = a^3$
- Cuboid: $V = l \times b \times h$
- Cylinder: $V = \pi r^2 h$
- Cone: $V = \frac{1}{3} \pi r^2 h$
- Sphere: $V = \frac{4}{3} \pi r^3$
Example: Find the volume of a cylinder with radius 3 cm and height 7 cm.
$$ V = \pi r^2 h = 3.14 \times 3^2 \times 7 = 3.14 \times 9 \times 7 = 197.82 \text{ cm}^3 $$
Difference Between Surface Area and Volume
Understanding the difference between surface area and volume is crucial:
| Aspect | Surface Area | Volume |
|---|---|---|
| Definition | Total area covering the outer surface | Space occupied inside the solid |
| Unit | Square units (cm², m²) | Cubic units (cm³, m³) |
| Example | Paint needed to cover a box | Water that can fill the box |
Surface area relates to covering or wrapping, while volume relates to capacity or space inside.
Practical Applications of Mensuration for Class 8 Students
Mensuration is not just theoretical; it has many practical uses:
- Calculating the amount of paint needed to cover walls (surface area)
- Determining the carpet size required for a floor (area)
- Finding the capacity of containers like water tanks (volume)
- Estimating fencing length around a garden (perimeter)
These applications help students see the relevance of mensuration in daily life and various professions like architecture, engineering, and design.
Frequently asked questions
What is mensuration in Class 8 maths?
Mensuration is the study of measuring lengths, areas, surface areas, and volumes of geometric shapes.
Which shapes are covered in Class 8 mensuration?
Class 8 covers squares, rectangles, triangles, circles, cubes, cuboids, cylinders, cones, and spheres.
How do you find the volume of a cylinder?
Volume of a cylinder is $V = \pi r^2 h$, where $r$ is radius and $h$ is height.
What is the difference between surface area and volume?
Surface area is the total outer area; volume is the space inside a 3D object.
Why is mensuration important for Class 8 students?
It helps solve real-life problems involving measurement and prepares students for exams.
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