Solids Class 6 ICSE — Maths Chapter 24
Solids class 6 ICSE maths explains how to describe objects that occupy space. This chapter from the Class 6 ICSE Mathematics book defines what a solid is. It teaches you to count faces, edges and vertices of prisms, pyramids, cuboids and cubes. It also gives the volume and surface area formulas for cuboid and cube. You will use these ideas again in later chapters on mensuration.
Download Solids Class 6 ICSE Mathematics Chapter 24 PDF
Download the Solids Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 9 pages, 3 sections, 27 questions.
What is inside Chapter 24
9 pages · 3 sections · 16 worked examples · 27 exercise questions
| Section | Title |
|---|---|
| 24.1 | SOLID |
| 24.2 | RECOGNIZING FACES, EDGES AND VERTICES (CORNERS) OF SOME SOLIDS |
| 24.3 | VOLUME AND SURFACE OF CUBOID AND CUBE |
- EXERCISE 24(A): 12 questions
- EXERCISE 24(B): 6 questions
- Revision Exercise (Chapter 24): 9 questions
24.1 SOLID
An object that occupies space is called a solid. A book, a brick and a ball are all solids. So are a pencil box, a water bottle and a cricket ball. They each have length, breadth and height. This is why every solid is a three-dimensional figure.
The chapter builds this idea step by step. A thin straight line on paper has only length. So a line has one dimension. A rectangle drawn on paper has length and breadth. So it has two dimensions. Every figure drawn on a plane is two-dimensional. You met plane figures in the previous chapter of your Class 6 ICSE Maths book.
A solid adds height to length and breadth. That third dimension is what separates solids from plane figures. When you measure a room, you need all three. When you draw a square, you only need length and breadth. Height is also called thickness or depth in some problems.
The word solid in this chapter does not mean hard or firm. It means any object that takes up space. Once you fix this definition, counting faces, edges and vertices becomes a matter of careful observation.
24.2 RECOGNIZING FACES, EDGES AND VERTICES (CORNERS) OF SOME SOLIDS
The chapter names and counts the faces, edges and vertices of four solids. A face is a flat surface. An edge is where two faces meet. A vertex is a corner where edges meet.
A prism has two parallel and congruent bases. A triangular prism has three side faces, nine edges and six vertices. A pentagonal prism has five side faces, fifteen edges and ten vertices. The side faces are parallelograms or rectangles.
A pyramid has a plane rectilinear base. Its side faces are triangles with a common vertex. That common vertex lies outside the plane of the base. A pyramid is named by its base. A triangular base gives a triangular pyramid. A quadrilateral base gives a quadrilateral pyramid.
A cuboid is a rectangular solid. It has six rectangular faces, twelve edges and eight vertices. Its edges fall into three equal groups. The length edges are all equal. The breadth edges are all equal. The height edges are all equal.
A cube is a cuboid with all sides equal. It has six congruent square faces, twelve edges and eight corners. Every edge of a cube has the same length.
| Property | Cuboid | Cube |
|---|---|---|
| Faces | 6 rectangles | 6 squares, all congruent |
| Edges | 12, in 3 equal groups | 12, all equal |
| Vertices | 8 | 8 |
| Volume | l \times b \times h | a^3 |
| Surface area | 2(lb + bh + hl) | 6a^2 |
24.3 VOLUME AND SURFACE OF CUBOID AND CUBE
The volume of a solid is the measure of the space it occupies. For a cuboid, the volume is the product of its length, breadth and height.
V = l \times b \times h \text{ unit}^3
A cube has length = breadth = height = a. So its volume is the cube of its side.
V = a \times a \times a = a^3 \text{ unit}^3
The volume formula can be rearranged. To find a missing dimension, divide the volume by the product of the other two dimensions.
l = \frac{V}{b \times h}, \quad b = \frac{V}{l \times h}, \quad h = \frac{V}{l \times b}
The surface area of a solid is the sum of the areas of all its faces. A cuboid has three pairs of equal opposite faces. So its surface area is double the sum of the three face areas.
2(l \times b + b \times h + h \times l)
A cube has six equal square faces. Each face has area a^2. So its surface area is 6a^2.
Units matter in every answer. When dimensions are in centimetres, volume is in \text{cm}^3. When dimensions are in metres, volume is in \text{m}^3. Also, 1 \text{ m} = 100 \text{ cm}, and 1 \text{ m}^3 = 100 \times 100 \times 100 \text{ cm}^3.
Worked example pattern: take a cuboid with length 10 cm, breadth 4 cm and height 3 cm. Its volume is 10 \times 4 \times 3 = 120 \text{ cm}^3. Its surface area is 2(10 \times 4 + 4 \times 3 + 3 \times 10) = 2(40 + 12 + 30) = 164 \text{ cm}^2.
Melting and recast pattern: when a solid is melted and recast, its volume stays the same. The number of smaller pieces equals the original volume divided by the volume of each piece. Take a cuboid 20 \text{ cm} \times 15 \text{ cm} \times 10 \text{ cm} melted into cubes of edge 5 cm. Number of cubes = \frac{20 \times 15 \times 10}{5^3} = 24.
Capacity in litres: 1 \text{ m}^3 = 1000 litres. To convert a volume in \text{m}^3 to litres, multiply by 1000. Mnemonic: think of a cubic metre as a large water tank and a litre as a small bottle. One cubic metre holds one thousand bottles.
Common mistakes to avoid:
- Mixing cm and m in one calculation. Convert all dimensions to the same unit first.
- Counting each face twice. A cuboid has six faces, not twelve.
- Using the cube formula for a cuboid. Check whether all sides are equal.
- Forgetting the unit in the final answer. Volume needs \text{unit}^3.
What to practise from Solids Class 6 ICSE
The exercise blocks in this ICSE chapter test the skills in order. Work through them after you finish section 24.3. The table maps each block to the concept it tests.
| Exercise | Questions | What it tests |
|---|---|---|
| EXERCISE 24(A) | 12 | Naming solids; faces, edges and vertices; areas of individual cuboid faces; volume and surface area tables |
| EXERCISE 24(B) | 6 | Capacity in litres; cutting cubes from a block; bricks for a pile; equal volumes |
| Revision Exercise (Chapter 24) | 9 | Surface area and painting cost; height from volume; tank and pool capacity; melting and recast; least bricks |
For more practice on the same ideas, browse the full set of Class 6 ICSE Maths chapters. Check the official CISCE website for the syllabus of this chapter.
Solids Class 6 ICSE frequently asked questions
What is a solid in solids class 6 ICSE?
A solid is an object that occupies space. A book, a brick and a ball are solids. Every solid has length, breadth and height, so it is a three-dimensional figure.
How many faces, edges and vertices does a cuboid have in Class 6 ICSE Maths?
A cuboid has six rectangular faces, twelve edges and eight vertices. Its edges form three equal groups: length, breadth and height. A cube is the special case where all twelve edges are equal.
What is the formula for the volume of a cube in class 6 ICSE?
The volume of a cube is a^3, where a is the length of one side. Since all sides of a cube are equal, you multiply the side by itself three times.
How do I convert cubic metres to litres in this ICSE chapter?
Multiply the volume in cubic metres by 1000. One cubic metre equals one thousand litres. A tank of volume 2.4 \text{ m}^3 holds 2400 litres.
How do I solve melting and recast problems in this ICSE chapter?
Melting does not change volume. Divide the original volume by the volume of each smaller piece. That gives the number of pieces formed.
Reference: ICSE Class 6 Mathematics textbook material, chapter 24: Solids — CISCE-aligned.