Mathematics · Class 8
Visualising Solid Shapes
Euler's formula, mapping space around us, and polyhedron views.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Class 8 revisits 3D shapes with views (front, side, top), maps, polyhedrons, prisms, pyramids, and Euler's formula — spatial reasoning for higher geometry.
Views of Solids
- Front view, side view, top view sketch 3D on 2D
- Different views may look different
Polyhedrons
- Faces are polygons only
- Prism: two congruent parallel bases
- Pyramid: polygon base + triangular faces to apex
Euler's Formula
Euler
F + V − E = 2
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Views
A cuboid 4×3×2. Top view shape?
- 1Look from above
Answer
Rectangle 4 × 3
Example 2: Euler
Triangular prism: F=5, V=6. Find E.
- 1F+V−E=2
- 25+6−E=2
- 3E=9
Answer
9 edges
Key Points to Remember
- ✓ Convex polyhedron satisfies Euler formula
- ✓ Map scale connects distance on map to ground
- ✓ Platonic solids are regular polyhedrons
Exam Tips
- • Sketch three views separately
- • Verify Euler for polyhedrons
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
F+V−E for convex polyhedron equals: