Recognition of Solids (Representing 3-D in 2-D)
ICSE Class 7 · Mathematics · Chapter 18
What this chapter covers
- Plane figures and solid shapes
- Faces, edges and vertices
- Nets of solids
- Drawing solids on a flat surface
- Estimating the space around you
Key points
- A plane figure has two dimensions; a solid has three and occupies space.
- A face is a flat surface of a solid, an edge is where two faces meet, and a vertex is a corner where edges meet.
- A cube and a cuboid each have 6 faces, 12 edges and 8 vertices.
- A cylinder has 2 flat faces and 1 curved surface; a cone has 1 flat face, 1 curved surface and 1 vertex; a sphere has 1 curved surface only.
- A net is a flat pattern that folds into a solid; a cube has 11 different nets.
- The net of a cuboid has three pairs of equal rectangles; the net of a cylinder is a rectangle and two circles; the net of a cone is a sector and a circle.
- An oblique sketch keeps the front face true; an isometric sketch keeps every edge length true.
- Hidden edges are shown with dashed lines.
- Estimation compares an unknown size with a known one, such as a door, a step or a cricket pitch.
- A rough map shows places from above, in the right order, with the right turns and roughly the right distances.
Questions answered
What is the difference between a plane figure and a solid? Give one example of each.
A plane figure lies flat and has only length and breadth, such as a triangle. A solid occupies space and has length, breadth and height, such as a brick.
How many faces, edges and vertices does a triangular prism have?
5 faces (2 triangles and 3 rectangles), 9 edges (3 + 3 + 3) and 6 vertices (3 + 3).
Which solid has one flat face, one curved surface and one vertex?
A cone.
A student says a sphere has one face. Is the student right?
Not quite. A sphere has no flat face at all; it has one curved surface, no edges and no vertices.
Six squares are joined in a straight row. Can they be folded into a cube? Give a reason.
No. The first four squares form the walls of a square tube, the fifth and sixth squares fall back onto the first and second, and both ends of the tube stay open.
Which plane shapes make up the net of a closed cylinder? How long must the rectangle be?
One rectangle and two equal circles. The rectangle's length must equal the distance round each circle, and its breadth equals the height of the cylinder.
Describe the net of a cone.
A sector of a circle, which forms the curved surface, with a small circle attached to its curved edge, which forms the base.
List the rectangles in the net of a closed cuboid 10 cm by 5 cm by 4 cm.
Two rectangles of 10 cm by 5 cm, two of 10 cm by 4 cm and two of 5 cm by 4 cm.