Learn to picture 3D solids from different views, and represent them using flat 2D drawings and nets.
Every solid has faces (flat or curved surfaces), edges (where two faces meet), and vertices (corner points where edges meet). Euler's formula connects them: Faces + Vertices − Edges = 2, for solids with flat faces.
A cube has 6 faces and 8 vertices. Use Euler's formula to find its edges.
6 + 8 − E = 2, so E = 12
A square pyramid has 5 faces and 5 vertices. Use Euler's formula to find its edges.
5 + 5 − E = 2, so E = 8
A solid can be drawn from the front, side, and top to show its shape from different angles. A net is a 2D shape that, when folded along its edges, forms a 3D solid.
What does the top view of a cylinder standing upright look like?
A circle
How many rectangular faces does the net of a cube have?
6 squares, all congruent
1. A triangular prism has 5 faces and 6 vertices. Use Euler's formula to find its edges.
2. A hexagonal pyramid has 7 faces and 7 vertices. Use Euler's formula to find its edges.
3. What does the front view of a cone look like?
4. What does the side view of a cube look like?
5. How many faces does the net of a triangular pyramid (tetrahedron) have?