Educational worksheet for students to practice drawing cross sections of various 3D shapes.

To solve the problem of determining the 2D shapes created by slicing each 3D shape, we need to analyze how a plane intersects with each given 3D shape. Let's go through each shape step by step:

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1. Cylinder

- Shape: A cylinder is a 3D shape with two parallel circular bases connected by a curved surface.
- Cross Section:
- If the plane cuts the cylinder parallel to its base, the cross section will be a circle.
- If the plane cuts the cylinder perpendicular to its axis, the cross section will be a rectangle (or a square if the cylinder is a right circular cylinder and the plane is exactly in the middle).
- If the plane cuts at an angle, the cross section can be an ellipse.

For this worksheet, the most common and straightforward cross section is when the plane is parallel to the base:
- Answer: Circle

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2. Cone

- Shape: A cone is a 3D shape with a circular base and a single vertex (apex) that tapers smoothly from the base to the apex.
- Cross Section:
- If the plane cuts the cone parallel to the base, the cross section will be a circle.
- If the plane cuts the cone perpendicular to the axis and passes through the apex, the cross section will be a triangle.
- If the plane cuts the cone at an angle but does not pass through the apex, the cross section can be an ellipse or a parabola depending on the angle.

For this worksheet, the most common and straightforward cross section is when the plane is parallel to the base:
- Answer: Circle

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3. Pentagonal Prism

- Shape: A pentagonal prism is a 3D shape with two parallel pentagonal bases and rectangular lateral faces.
- Cross Section:
- If the plane cuts the prism parallel to one of the pentagonal bases, the cross section will be a pentagon.
- If the plane cuts the prism perpendicular to the axis, the cross section will be a rectangle.
- Other angled cuts can produce more complex shapes, but the most straightforward is parallel to the base.

For this worksheet, the most common and straightforward cross section is when the plane is parallel to the base:
- Answer: Pentagon

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4. Hexagonal Prism

- Shape: A hexagonal prism is a 3D shape with two parallel hexagonal bases and rectangular lateral faces.
- Cross Section:
- If the plane cuts the prism parallel to one of the hexagonal bases, the cross section will be a hexagon.
- If the plane cuts the prism perpendicular to the axis, the cross section will be a rectangle.
- Other angled cuts can produce more complex shapes, but the most straightforward is parallel to the base.

For this worksheet, the most common and straightforward cross section is when the plane is parallel to the base:
- Answer: Hexagon

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5. Triangular Prism

- Shape: A triangular prism is a 3D shape with two parallel triangular bases and rectangular lateral faces.
- Cross Section:
- If the plane cuts the prism parallel to one of the triangular bases, the cross section will be a triangle.
- If the plane cuts the prism perpendicular to the axis, the cross section will be a rectangle.
- Other angled cuts can produce more complex shapes, but the most straightforward is parallel to the base.

For this worksheet, the most common and straightforward cross section is when the plane is parallel to the base:
- Answer: Triangle

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Final Answers

1. Cylinder: Circle
2. Cone: Circle
3. Pentagonal Prism: Pentagon
4. Hexagonal Prism: Hexagon
5. Triangular Prism: Triangle

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Summary Table

| Shape | Cross Section |
|---------------------|---------------|
| Cylinder | Circle |
| Cone | Circle |
| Pentagonal Prism | Pentagon |
| Hexagonal Prism | Hexagon |
| Triangular Prism | Triangle |

Final Answer:
$$
\boxed{
\begin{array}{|c|c|}
\hline
\text{Shape} & \text{Cross Section} \\
\hline
\text{Cylinder} & \text{Circle} \\
\text{Cone} & \text{Circle} \\
\text{Pentagonal Prism} & \text{Pentagon} \\
\text{Hexagonal Prism} & \text{Hexagon} \\
\text{Triangular Prism} & \text{Triangle} \\
\hline
\end{array}
}
$$