Mathematics · Class 7
Visualising Solid Shapes
Faces, edges, vertices, nets, and different views of 3D solids.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Visualise 3D shapes through faces, edges, vertices, nets, oblique sketches, and isometric dot sheets — bridge from plane geometry to solids.
Euler's Formula
Euler
F + V = E + 2 (Faces + Vertices = Edges + 2)
Nets
- Net: flattened 2D pattern that folds into 3D solid
- Cube has 11 distinct nets
- Identify valid nets by checking adjacent faces
Drawing Solids
- Oblique sketch: front face true shape, depth at angle
- Isometric sketch: equal angles, use isometric dot paper
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Euler's Formula
A solid has 6 faces and 8 vertices. Find edges.
- 1F + V = E + 2
- 26 + 8 = E + 2
- 3E = 12
Answer
12 edges
Example 2: Identify Solid
A solid has 1 curved surface and 2 circular faces.
- 1Two parallel circular faces + curved surface
Answer
Cylinder
Key Points to Remember
- ✓ Verify nets by mental folding
- ✓ Prism: two identical polygon bases
- ✓ Pyramid: polygon base + triangular faces meeting at apex
Exam Tips
- • Count faces, edges, vertices systematically
- • Use Euler formula to check answers
Practice MCQs — Visualising Solid Shapes
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Euler's formula is: