Practice worksheet for identifying cross sections of 3D shapes.

Problem Overview:

The task is to identify the 2D cross-sections formed when each 3D shape is cut parallel and perpendicular to its base. Let's solve this step by step for each shape.

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1. Rectangular Prism

- Parallel to Base: The base of a rectangular prism is a rectangle. Cutting parallel to the base will result in another rectangle.
- Perpendicular to Base: Cutting perpendicular to the base will result in a rectangle (since all faces are rectangles).

Answer:
- Parallel to base: Rectangle
- Perpendicular to base: Rectangle

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2. Cylinder

- Parallel to Base: The base of a cylinder is a circle. Cutting parallel to the base will result in another circle.
- Perpendicular to Base: Cutting perpendicular to the base will result in a rectangle (the height of the cylinder forms one side, and the diameter of the circular base forms the other).

Answer:
- Parallel to base: Circle
- Perpendicular to base: Rectangle

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3. Pyramid

- Parallel to Base: The base of a pyramid is a polygon (in this case, a triangle). Cutting parallel to the base will result in a smaller triangle (similar to the base).
- Perpendicular to Base: Cutting perpendicular to the base will result in a triangle (a triangular face of the pyramid).

Answer:
- Parallel to base: Triangle
- Perpendicular to base: Triangle

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4. Triangular Prism

- Parallel to Base: The base of a triangular prism is a triangle. Cutting parallel to the base will result in another triangle.
- Perpendicular to Base: Cutting perpendicular to the base will result in a rectangle (formed by the height of the prism and the length of the triangular base).

Answer:
- Parallel to base: Triangle
- Perpendicular to base: Rectangle

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5. Sphere

- Parallel to Base: A sphere does not have a "base" in the traditional sense, but cutting it horizontally (parallel to any plane) will always result in a circle.
- Perpendicular to Base: Similarly, cutting a sphere vertically (perpendicular to any plane) will also result in a circle.

Answer:
- Parallel to base: Circle
- Perpendicular to base: Circle

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6. Trapezoidal Prism

- Parallel to Base: The base of a trapezoidal prism is a trapezoid. Cutting parallel to the base will result in another trapezoid.
- Perpendicular to Base: Cutting perpendicular to the base will result in a rectangle (formed by the height of the prism and the length of the trapezoidal base).

Answer:
- Parallel to base: Trapezoid
- Perpendicular to base: Rectangle

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7. Cube

- Parallel to Base: The base of a cube is a square. Cutting parallel to the base will result in another square.
- Perpendicular to Base: Cutting perpendicular to the base will result in a square (since all faces are squares).

Answer:
- Parallel to base: Square
- Perpendicular to base: Square

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8. Cone

- Parallel to Base: The base of a cone is a circle. Cutting parallel to the base will result in another circle.
- Perpendicular to Base: Cutting perpendicular to the base will result in a triangle (the cross-section includes the apex and the diameter of the base).

Answer:
- Parallel to base: Circle
- Perpendicular to base: Triangle

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9. Triangular Pyramid

- Parallel to Base: The base of a triangular pyramid is a triangle. Cutting parallel to the base will result in another triangle (similar to the base).
- Perpendicular to Base: Cutting perpendicular to the base will result in a triangle (a triangular face of the pyramid).

Answer:
- Parallel to base: Triangle
- Perpendicular to base: Triangle

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10. Cube

- Parallel to Base: The base of a cube is a square. Cutting parallel to the base will result in another square.
- Perpendicular to Base: Cutting perpendicular to the base will result in a square (since all faces are squares).

Answer:
- Parallel to base: Square
- Perpendicular to base: Square

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11. Hexagonal Prism

- Parallel to Base: The base of a hexagonal prism is a hexagon. Cutting parallel to the base will result in another hexagon.
- Perpendicular to Base: Cutting perpendicular to the base will result in a rectangle (formed by the height of the prism and the length of the hexagonal base).

Answer:
- Parallel to base: Hexagon
- Perpendicular to base: Rectangle

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12. Tetrahedron

- Parallel to Base: The base of a tetrahedron is a triangle. Cutting parallel to the base will result in another triangle (similar to the base).
- Perpendicular to Base: Cutting perpendicular to the base will result in a triangle (a triangular face of the tetrahedron).

Answer:
- Parallel to base: Triangle
- Perpendicular to base: Triangle

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Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|}
\hline
\text{Shape} & \text{Parallel to Base} & \text{Perpendicular to Base} \\
\hline
1. \text{Rectangular Prism} & \text{Rectangle} & \text{Rectangle} \\
2. \text{Cylinder} & \text{Circle} & \text{Rectangle} \\
3. \text{Pyramid} & \text{Triangle} & \text{Triangle} \\
4. \text{Triangular Prism} & \text{Triangle} & \text{Rectangle} \\
5. \text{Sphere} & \text{Circle} & \text{Circle} \\
6. \text{Trapezoidal Prism} & \text{Trapezoid} & \text{Rectangle} \\
7. \text{Cube} & \text{Square} & \text{Square} \\
8. \text{Cone} & \text{Circle} & \text{Triangle} \\
9. \text{Triangular Pyramid} & \text{Triangle} & \text{Triangle} \\
10. \text{Cube} & \text{Square} & \text{Square} \\
11. \text{Hexagonal Prism} & \text{Hexagon} & \text{Rectangle} \\
12. \text{Tetrahedron} & \text{Triangle} & \text{Triangle} \\
\hline
\end{array}
}
\]