Visualising Solid Shapes
Nets of 3D Shapes
A net is a flat shape that folds up into a solid. The net of a cube is 6 squares; a cuboid is 6 rectangles; a cylinder is 2 circles and 1 rectangle; and a cone is 1 circle and 1 curved sector.
Example 1: How many squares are in the net of a cube?
6 squares.
Example 2: What does the net of a cylinder contain?
2 circles and 1 rectangle.
Quick recap
- Cube net = 6 squares; cuboid net = 6 rectangles.
- Cylinder net = 2 circles + 1 rectangle; cone net = 1 circle + 1 sector.
✓ Quick check
How many faces does the net of a cuboid have?
A cuboid has 6 faces.
A cone's net has a circle and a ___ ?
A cone's curved surface opens into a sector.
Sketches & Solid Properties
An isometric sketch is drawn on a dotted grid keeping true lengths; an oblique sketch shows the front face true with the depth slanted. Recall: a cube has 6 faces, 12 edges and 8 vertices.
Example 1: How many edges does a cube have?
12 edges.
Example 2: How many vertices does a cuboid have?
8 vertices.
Quick recap
- Isometric: true lengths on a dotted grid; oblique: front true, depth slanted.
- Cube/cuboid: 6 faces, 12 edges, 8 vertices.
✓ Quick check
How many faces does a cube have?
A cube has 6 faces.
How many vertices does a cube have?
A cube has 8 vertices.
Views of 3D Objects
A solid object can be drawn from different views: the front view, the side view and the top view. For example, the top view of a standing cylinder is a circle, and the front view of a cube is a square.
Example 1: What is the top view of a standing cylinder?
A circle.
Example 2: What is the front view of a cube?
A square.
Quick recap
- Objects have front, side and top views.
- Top view of a cylinder = circle; front view of a cube = square.
✓ Quick check
What is the top view of a ball (sphere)?
From any direction a sphere looks like a circle.
What is the side view of a cube?
A cube's side view is a square.
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