Solids Around Us (3-D Shapes) • Topic 2 of 4

Properties of Solids

Once a child can name the solids, the next step is to describe them precisely using three words: face, edge and vertex. A face is a surface that bounds the solid. It can be flat, like the side of a dice or the top of a table, or curved, like the round body of a water pipe or the surface of a ball. An edge is the line where two faces meet - the seam of the solid. Edges are usually straight, as on a cube or cuboid, but they can also be circular, such as the rim where the curved surface of a cylinder meets one of its circular ends. A vertex, or corner, is a point where edges come together; it is usually a sharp point, and the plural is vertices. Now apply these to the five solids. A cube and a cuboid both have 6 flat faces, 12 straight edges and 8 vertices. A cylinder has 3 faces in total - 2 flat circles plus 1 curved surface - along with 2 circular edges and no vertices, because nothing comes to a point. A cone has 2 faces (1 flat circle and 1 curved surface), 1 circular edge and exactly 1 vertex, the apex at the tip. A sphere is the simplest to describe and the easiest to get wrong: it has just 1 curved surface, 0 edges and 0 vertices, since its surface never breaks into separate faces. For CTET the three numbers that catch people out are the cylinder (3 faces, not 2), the cone (1 vertex, not 0), and the sphere (0 edges and 0 vertices).

✅ Solved examples

1. How many faces, edges and vertices does a cylinder have?
3 faces (two flat circles plus one curved surface), 2 edges (the two circular rims) and 0 vertices. It has no corners because nothing comes to a point.
2. A solid has 1 flat face, 1 curved face, 1 edge and 1 vertex. Which solid is it?
A cone. The flat face is the circular base, the edge is the rim of that base, and the single vertex is the apex at the top.
3. Why does a sphere have no edges and no vertices?
An edge needs two faces to meet and a vertex needs edges to meet at a point. A sphere has only one continuous curved surface, so there are no meeting lines and no corners - 0 edges and 0 vertices.
4. A cube and a cuboid share the same count of faces, edges and vertices. What are those counts, and what makes their faces different?
Both have 6 faces, 12 edges and 8 vertices. The cube's faces are all equal squares, while the cuboid's faces are rectangles (its dimensions usually differ).

✏️ Practice — try these, take hints as needed

1. Define an edge and give one example of a curved edge.
An edge is where two faces meet.
Look at where a cylinder's flat circle meets its curved surface.
An edge is the line where two faces meet; the circular rim of a cylinder (or the base of a cone) is a curved edge
2. How many vertices does a cone have, and where is it located?
It is not zero.
Think of the sharp tip.
1 vertex, located at the apex (the pointed tip)
3. Which two solids have exactly 6 flat faces, 12 edges and 8 vertices?
Both are box-shaped.
One has square faces, the other rectangular.
Cube and cuboid
4. A teacher asks: "How many flat faces does a sphere have?" What is the correct answer and why?
A sphere is round all over.
Count only flat surfaces.
0 flat faces - a sphere has only one curved surface and no flat part

📝 Topic test — 8 questions

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