wunder beta

🧊 Faces, Edges, and Cross-Sections of 3D Shapes

Count the faces, edges, and vertices of solids like cubes and pyramids — then slice them open to reveal the 2D cross-sections hiding inside.

lessons

~15 min

to learn

🔢 Math

subject

Teens

level

Start the course →

What you’ll learn

Faces, Edges, and VerticesIdentify and count the faces, edges, and vertices of common solids and check Euler's formula.Solids are three-dimensional shapes described by three features: a face is a flat surface, an edge is the line where two faces meet, and a vertex is a corner. A cube has 6 faces, 12 edges, and 8 vertices; other solids have their own counts. Euler's formula, F + V = E + 2, holds true for every polyhedron.
Slicing Into Cross-SectionsPredict the 2D cross-section produced by slicing through a solid.A cross-section is the flat 2D shape revealed when you slice straight through a solid. A cube sliced parallel to a face gives a square, a cylinder or cone sliced across gives a circle, and every slice through a sphere is a circle. The cross-section depends on both the solid and the angle of the cut.

Questions this course answers

What is an edge of a solid?

An edge is the straight line formed where two faces of a solid meet.

How many vertices (corners) does a cube have?

A cube has 8 vertices — one at each of its eight corners.

A square-based pyramid has how many faces?

A square-based pyramid has 1 square base plus 4 triangular sides, giving 5 faces in all.

Euler's formula says that for a solid with flat faces, F + V equals what?

Euler's formula states F + V = E + 2 for every polyhedron.

What is a cross-section?

A cross-section is the flat two-dimensional shape you see on the fresh cut when you slice through a solid.

If you slice a cylinder straight across, what cross-section do you get?

Cutting straight across a cylinder reveals a circle, the same shape as its round ends.

Grounded in trusted sources

Khan Academy — 3D figures and cross-sections
National Council of Teachers of Mathematics
Britannica — polyhedron
BBC Bitesize — 3D shapes

Every Wunder lesson is built from real, reputable sources — never invented.

Related Math courses

🧊Edges, Vertices, and Faces 🧊Drawing and Classifying 2D and 3D Shapes 🍬Finding Fractions of Any Amount 🍎Finding Halves 📐Finding Missing Angles 🔎Finding Missing Angles and Sides 🔢Finding Patterns in Times Tables 🍕Finding Quarters

Wunder is a personalized learn-anything platform — tell it any topic and it builds a beautiful, fact-checked course in minutes, with narration, a knowledge check, and a college-style University track.

Browse more Math courses · All topics · Home