Here are the solutions for the properties of the 3D shapes.
1) Rectangular Prism (Cuboid)
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Name: Rectangular Prism
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Vertices: 8
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Faces: 6
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Edges: 12
2) Triangular Prism
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Name: Triangular Prism
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Vertices: 6
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Faces: 5
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Edges: 9
3) Cone
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Name: Cone
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Vertices: 1 (the apex at the top)
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Faces: 2 (1 flat circular base + 1 curved surface)
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Edges: 1 (the circular edge around the base)
4) Square-based Pyramid
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Name: Square-based Pyramid
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Vertices: 5
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Faces: 5
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Edges: 8
5) Cylinder
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Name: Cylinder
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Vertices: 0
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Faces: 3 (2 flat circular ends + 1 curved surface)
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Edges: 2 (the two circular edges)
6) Cube
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Name: Cube
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Vertices: 8
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Faces: 6
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Edges: 12
7) Sphere
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Name: Sphere
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Vertices: 0
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Faces: 1 (the single curved surface)
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Edges: 0
8) Octahedron (Square Bipyramid)
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Name: Octahedron
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Vertices: 6
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Faces: 8
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Edges: 12
9) Pentagonal Prism
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Name: Pentagonal Prism
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Vertices: 10
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Faces: 7 (5 rectangular sides + 2 pentagon bases)
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Edges: 15
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Extension Section
A) Hexagonal Prism
* *Reasoning:* It has 12 vertices and 8 faces. A prism with an $n$-sided base has $2n$ vertices and $n+2$ faces. Here, $2n=12$, so $n=6$.
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Name: Hexagonal Prism
B) Octagonal Prism
* *Reasoning:* It has 16 vertices. Since it is a prism, $2n = 16$, which means $n=8$. An 8-sided base makes it an octagonal prism.
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Name: Octagonal Prism
C) Pentagonal Pyramid
* *Reasoning:* It has 6 vertices. A pyramid with an $n$-sided base has $n+1$ vertices. Here, $n+1=6$, so $n=5$. A 5-sided base makes it a pentagonal pyramid.
*
Name: Pentagonal Pyramid
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Final Answer:
1) Name: Rectangular Prism, Vertices: 8, Faces: 6, Edges: 12
2) Name: Triangular Prism, Vertices: 6, Faces: 5, Edges: 9
3) Name: Cone, Vertices: 1, Faces: 2, Edges: 1
4) Name: Square-based Pyramid, Vertices: 5, Faces: 5, Edges: 8
5) Name: Cylinder, Vertices: 0, Faces: 3, Edges: 2
6) Name: Cube, Vertices: 8, Faces: 6, Edges: 12
7) Name: Sphere, Vertices: 0, Faces: 1, Edges: 0
8) Name: Octahedron, Vertices: 6, Faces: 8, Edges: 12
9) Name: Pentagonal Prism, Vertices: 10, Faces: 7, Edges: 15
Extension:
A) Name: Hexagonal Prism
B) Name: Octagonal Prism
C) Name: Pentagonal Pyramid
Parent Tip: Review the logic above to help your child master the concept of name 3d shapes worksheet.
