Edexcel Mathematics (4XMAF) -Unit 1 - 4.10 3D Shapes and Volume- Study Notes- New Syllabus
Edexcel Mathematics (4XMAF) -Unit 1 – 4.10 3D Shapes and Volume- Study Notes- New syllabus
Edexcel Mathematics (4XMAF) -Unit 1 – 4.10 3D Shapes and Volume- Study Notes -Edexcel iGCSE Mathematics – per latest Syllabus.
Key Concepts:
A recognise and give the names of solids
Notes: cube, cuboid, prism, pyramid, cylinder, sphere and cone
B understand the terms ‘face’, ‘edge’ and ‘vertex’ in the context of 3D solids
Edexcel iGCSE Mathematics -Concise Summary Notes- All Topics
Names of 3D Solids
A 3D solid is a shape that has length, width and height (depth). Unlike 2D shapes, 3D shapes have volume.
Common Solids
- Cube
- Cuboid
- Prism
- Pyramid
- Cylinder
- Sphere
- Cone
Descriptions
- Cube: All edges equal, all faces squares
- Cuboid: Box-shaped, rectangular faces
- Prism: Same cross-section throughout
- Pyramid: Triangular faces meet at a point
- Cylinder: Two circular ends and one curved surface
- Sphere: Perfect ball shape
- Cone: Circular base with a pointed top
Key Idea
A prism keeps the same cross-section all the way through.
Example 1:
A solid has six square faces of equal size. Name the solid.
▶️ Answer/Explanation
Six equal square faces.
Conclusion: Cube.
Example 2:
A solid has a circular base and a pointed top. Name the solid.
▶️ Answer/Explanation
Circular base and one vertex.
Conclusion: Cone.
Example 3:
A solid has identical cross-sections throughout its length. Name the type of solid.
▶️ Answer/Explanation
Same cross-section throughout.
Conclusion: Prism.
Faces, Edges and Vertices
When describing 3D solids, we use the terms face, edge and vertex.
Face
A face is a flat surface of a solid shape.
Example: A cube has square faces.
Edge
An edge is the line where two faces meet.
Vertex
A vertex is a corner point where edges meet.
(Plural: vertices)
Examples
Important
Curved surfaces (like on a sphere or cylinder) are not flat faces.
Example 1:
How many vertices does a cube have?
▶️ Answer/Explanation
A cube has 8 corner points.
Conclusion: 8 vertices.
Example 2:
Name the part of a solid where two faces meet.
▶️ Answer/Explanation
Two faces meet along a line.
Conclusion: Edge.
Example 3:
Name the part of a solid that is a flat surface.
▶️ Answer/Explanation
A flat surface of a solid.
Conclusion: Face.