Class 7 · Chapter 15

Visualising Solid Shapes

3D shapes; faces, edges, vertices; nets; oblique and isometric sketches; Euler's formula.

Read the full chapter
Tip: open the NCERT PDF for the original chapter text alongside the notes here.
Detailed theory
2-D shapes have length and breadth (circle, square, triangle). 3-D solids also have height (cube, cylinder, sphere). Solids have faces, edges, vertices.
Key concepts & formulas
01
A polyhedron is a solid whose faces are polygons.
02
Cube: 66 faces, 1212 edges, 88 vertices.
03
Sphere: no vertices or edges; 11 curved surface.
04
Cylinder: 22 circular flat faces, 11 curved surface.
05
Euler's formula: F+VE=2F + V - E = 2 (for convex polyhedra).
Gyaan Maths — CBSE Class 6-10, built for board-toppers.
v1.1 · Feb 2026