What is Surface Areas and Volumes Class 10: Complete Guide
By ConceptScroll Team · Published on 19 June 2026 · 4 min read
What is Surface Areas and Volumes class 10? It is a crucial chapter in the NCERT Mathematics syllabus that deals with calculating the surface area and volume of 3D shapes like cubes, cylinders, cones, and spheres. Mastering these concepts is essential for your Class 10 exams.
Understanding Surface Areas and Volumes in Class 10 Maths
Surface Areas and Volumes is a vital chapter in the Class 10 NCERT Mathematics syllabus. It focuses on two main concepts:
- Surface Area: The total area covered by the surface of a three-dimensional (3D) object.
- Volume: The amount of space enclosed within a 3D object.
These concepts help you solve real-life problems involving solids like boxes, cylinders, cones, and spheres. Knowing how to calculate surface area and volume is essential for practical applications and exams alike.
This chapter builds on your earlier knowledge of geometry and introduces formulas to find surface areas and volumes of various solids.
Key Formulas for Surface Areas and Volumes of Common Solids
Here are the essential formulas you need to remember for Class 10 NCERT:
| Solid | Surface Area (SA) | Volume (V) |
|---|---|---|
| Cube | $6a^2$ | $a^3$ |
| Cuboid | $2(lb + bh + hl)$ | $lbh$ |
| Cylinder | $2\pi r(h + r)$ | $\pi r^2 h$ |
| Cone | $\pi r(l + r)$ | $\frac{1}{3}\pi r^2 h$ |
| Sphere | $4\pi r^2$ | $\frac{4}{3}\pi r^3$ |
Where:
- $a$ = side of cube
- $l$, $b$, $h$ = length, breadth, height of cuboid
- $r$ = radius
- $h$ = height
- $l$ = slant height (for cone)
Example: Calculate the volume of a cylinder with radius 7 cm and height 10 cm.
$$ V = \pi r^2 h = \pi \times 7^2 \times 10 = 1540 \text{ cm}^3 $$
Use $\pi = \frac{22}{7}$ for calculations.
Want to test yourself on Surface Areas and Volumes? Try our free quiz →
Difference Between Surface Area and Volume
Understanding the difference between surface area and volume is important:
- Surface Area is a measure of the total area that the surface of the object occupies. It is expressed in square units like $cm^2$, $m^2$.
- Volume is the measure of space inside the object. It is expressed in cubic units like $cm^3$, $m^3$.
| Feature | Surface Area | Volume |
|---|---|---|
| What it measures | Outer covering area | Space inside the object |
| Units | Square units ($cm^2$, $m^2$) | Cubic units ($cm^3$, $m^3$) |
| Example | Paint needed to cover a box | Water held inside a box |
This distinction helps in solving different types of problems in Class 10 Maths.
How to Calculate Surface Areas and Volumes: Step-by-Step Guide
Follow these steps to calculate surface area and volume:
1. Identify the solid shape: Cube, cuboid, cylinder, cone, or sphere. 2. Write down given dimensions: Length, breadth, height, radius, slant height. 3. Choose the correct formula from the list of formulas. 4. Substitute the values carefully into the formula. 5. Calculate the result using proper units.
Worked Example: Find the total surface area of a cuboid with length 8 cm, breadth 5 cm, and height 3 cm.
$$ SA = 2(lb + bh + hl) = 2(8 \times 5 + 5 \times 3 + 3 \times 8) $$ $$ = 2(40 + 15 + 24) = 2(79) = 158 \text{ cm}^2 $$
This method ensures accuracy and clarity in your exam answers.
Real-Life Applications of Surface Areas and Volumes
Surface Areas and Volumes have many practical uses:
- Construction: Calculating paint needed to cover walls (surface area).
- Packaging: Designing boxes and containers with specific volume.
- Manufacturing: Determining material required for making objects.
- Medicine: Calculating doses based on volume of liquids.
- Everyday life: Filling a swimming pool (volume), wrapping gifts (surface area).
Understanding these applications helps you appreciate the importance of this chapter beyond exams.
Tips to Score Well in Surface Areas and Volumes Class 10 Exam
To excel in this chapter, follow these tips:
- Memorise all key formulas thoroughly.
- Practice drawing 3D shapes to visualise problems.
- Solve NCERT textbook exercises and sample papers.
- Pay attention to units and convert them when needed.
- Use $\pi = \frac{22}{7}$ or 3.14 as instructed.
- Review solved examples to understand problem-solving steps.
Consistent practice will boost your confidence and improve your exam score.
Frequently asked questions
What is surface area in Class 10 Maths?
Surface area is the total area covering the outer surface of a 3D object, measured in square units.
How do you find the volume of a cylinder?
Volume of a cylinder is $\pi r^2 h$, where $r$ is radius and $h$ is height.
What is the difference between lateral surface area and total surface area?
Lateral surface area excludes the base(s), while total surface area includes all surfaces of the solid.
Which units are used for volume and surface area?
Surface area uses square units like $cm^2$, volume uses cubic units like $cm^3$.
Is the formula for surface area the same for all solids?
No, each solid like cube, sphere, or cone has its own specific surface area formula.
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