Problem Overview:
The task is to match the given 3D shapes with their corresponding nets. A
net is a 2D pattern that can be folded to form a 3D shape. The goal is to identify which net corresponds to each 3D shape listed in the table.
Solution Approach:
1.
Understand the Shapes and Their Nets:
- Each 3D shape has a unique net pattern.
- Analyze the structure of each net and match it with the correct 3D shape based on the number and arrangement of faces.
2.
Match Each Net to Its Corresponding 3D Shape:
- Carefully examine the nets and compare them with the descriptions of the 3D shapes.
Step-by-Step Matching:
####
Row 1:
1.
Cone:
- The net for a cone consists of a circular base and a sector (part of a circle) that forms the curved surface when folded.
- The first net in Row 1 matches this description: a circle connected to a sector.
2.
Cuboid:
- The net for a cuboid consists of six rectangles, with opposite faces being congruent.
- The second net in Row 1 shows six rectangles arranged in a way that they can fold into a cuboid.
3.
Hexagonal Prism:
- The net for a hexagonal prism consists of two hexagons (bases) and six rectangles (sides).
- The third net in Row 1 shows two hexagons connected by six rectangles.
####
Row 2:
4.
Cylinder:
- The net for a cylinder consists of two circles (bases) and a rectangle (curved surface).
- The first net in Row 2 shows two circles connected by a rectangle.
5.
Cube:
- The net for a cube consists of six squares, arranged in a way that they can fold into a cube.
- The second net in Row 2 shows six squares in a cross-like pattern.
6.
Hexagonal Pyramid:
- The net for a hexagonal pyramid consists of one hexagon (base) and six triangles (sides).
- The third net in Row 2 shows a hexagon surrounded by six triangles.
####
Row 3:
7.
Square-Based Pyramid:
- The net for a square-based pyramid consists of one square (base) and four triangles (sides).
- The first net in Row 3 shows a square surrounded by four triangles.
8.
Triangular Prism:
- The net for a triangular prism consists of two triangles (bases) and three rectangles (sides).
- The second net in Row 3 shows two triangles connected by three rectangles.
9.
Tetrahedron:
- The net for a tetrahedron consists of four equilateral triangles.
- The third net in Row 3 shows four triangles arranged in a way that they can fold into a tetrahedron.
Final Matchings:
-
Row 1:
- Cone
- Cuboid
- Hexagonal prism
-
Row 2:
- Cylinder
- Cube
- Hexagonal pyramid
-
Row 3:
- Square-based pyramid
- Triangular prism
- Tetrahedron
Final Answer:
\[
\boxed{
\begin{array}{ccc}
\text{Cone} & \text{Cuboid} & \text{Hexagonal prism} \\
\text{Cylinder} & \text{Cube} & \text{Hexagonal pyramid} \\
\text{Square-based pyramid} & \text{Triangular prism} & \text{Tetrahedron}
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of nets of prisms and pyramids worksheet.