Math Problem Statement

For each net below, select the solid above to which it folds. The options include a cube, a square pyramid, and a tetrahedron.

Solution

Let’s analyze the image step-by-step:

Solids:

  • Solid a: Cube (6 square faces)
  • Solid b: Square pyramid (square base, 4 triangular faces)
  • Solid c: Tetrahedron (4 triangular faces)

Nets:

  1. Net 1: This net has 6 square faces, which matches a cube. Thus, this net folds into Solid a.

  2. Net 2: This net has one triangle and one circular part; it doesn’t correspond to any of the solids shown. Thus, the correct answer for this net is None.

  3. Net 3: This net has 5 faces, with 4 triangular faces around a central square. It folds into a square pyramid. Thus, this net corresponds to Solid b.

  4. Net 4: This net consists of 4 triangular faces, which forms a tetrahedron. Thus, it matches Solid c.

Summary of Answers:

  1. Solid a (cube)
  2. None
  3. Solid b (square pyramid)
  4. Solid c (tetrahedron)

Would you like further explanation on any of the answers, or do you have any specific questions?

Follow-up questions:

  1. What are the properties of a cube in terms of its faces, edges, and vertices?
  2. Can you describe the net of a tetrahedron and how it folds?
  3. How does a square pyramid differ from a tetrahedron?
  4. How many edges and vertices does a square pyramid have?
  5. Can a cube have different types of nets, or is there only one possible net?

Tip:

Visualizing how a 2D net folds into a 3D shape is easier if you focus on the base and how the faces connect around it.

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Math Problem Analysis

Mathematical Concepts

Geometry
3D Shapes
Nets of Solids

Formulas

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Theorems

Euler's Polyhedron Formula

Suitable Grade Level

Grades 5-7