Educational worksheet for learning the properties of 3D shapes.

The task involves identifying and writing down the properties of various 3D shapes. Below is a detailed explanation of the properties for each shape, along with an organized solution.

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Properties of 3D Shapes

#### 1. Pyramid
- Definition: A pyramid is a polyhedron formed by connecting a polygonal base to a point called the apex.
- Properties:
- It has a polygonal base (e.g., triangular, square, pentagonal).
- All other faces are triangular and meet at a single vertex (the apex).
- The number of triangular faces equals the number of sides of the base plus one.
- It has edges where the triangular faces meet.
- It has vertices at the corners of the base and the apex.

#### 2. Cone
- Definition: A cone is a 3D shape that tapers smoothly from a flat base (usually circular) to a point called the apex or vertex.
- Properties:
- It has a circular base.
- It has a curved surface that connects the base to the apex.
- It has one vertex (the apex).
- It has one edge (the circular edge of the base).

#### 3. Sphere
- Definition: A sphere is a perfectly round 3D object, like a ball.
- Properties:
- It is completely symmetrical around its center.
- Every point on the surface is equidistant from the center.
- It has no edges or vertices.
- It has a curved surface.

#### 4. Cube
- Definition: A cube is a 3D shape with six square faces, twelve edges, and eight vertices.
- Properties:
- It has six faces, all of which are squares.
- All faces are equal in size.
- It has twelve edges, all of which are of equal length.
- It has eight vertices.
- All angles are right angles (90 degrees).

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Solution

Here is how you can fill out the worksheet:

#### Left Side: Questions
1. What are the properties of a pyramid?
- Polygonal base.
- Triangular faces meeting at a single apex.
- Edges and vertices.

2. What are the properties of a cone?
- Circular base.
- Curved surface.
- One vertex (apex).
- One edge (base edge).

3. What are the properties of a sphere?
- Completely symmetrical.
- No edges or vertices.
- Curved surface.
- All points on the surface are equidistant from the center.

4. What are the properties of a cube?
- Six square faces.
- Twelve edges.
- Eight vertices.
- All faces are equal in size.
- All angles are right angles.

#### Right Side: Answers
1. What are the properties of a pyramid?
- A pyramid has a polygonal base and triangular faces meeting at a single apex. It has edges and vertices.

2. What are the properties of a cone?
- A cone has a circular base, a curved surface, one vertex (apex), and one edge (base edge).

3. What are the properties of a sphere?
- A sphere is completely symmetrical, has no edges or vertices, and has a curved surface. All points on the surface are equidistant from the center.

4. What are the properties of a cube?
- A cube has six square faces, twelve edges, and eight vertices. All faces are equal in size, and all angles are right angles.

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Final Answer

\[
\boxed{
\begin{array}{l}
\text{Pyramid: Polygonal base, triangular faces, edges, vertices.} \\
\text{Cone: Circular base, curved surface, one vertex, one edge.} \\
\text{Sphere: Symmetrical, no edges or vertices, curved surface.} \\
\text{Cube: Six square faces, twelve edges, eight vertices, all faces equal.}
\end{array}
}
\]