R
Rishtaara
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?

  1. 1Look from above

Answer

Rectangle 4 × 3

Example 2: Euler

Triangular prism: F=5, V=6. Find E.

  1. 1F+V−E=2
  2. 25+6−E=2
  3. 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: