Grade 6 Three Dimensional Shapes

Step 1: Identify the shape:

A shape with all faces as squares is a cube.

Step 2: Count the faces:

A cube has 6 faces, all of which are squares.

Step 3: Count the edges:

A cube has 12 edges.

Step 4: Count the vertices:

A cube has 8 vertices.

Step 5: Verify using Euler’s formula:

Euler’s formula for polyhedra: \( F + V - E = 2 \).

\( 6 + 8 - 12 = 2 \), which holds true.

Step 6: Therefore, the shape is a cube with 6 faces, 12 edges, and 8 vertices.

Step 1: Identify the shape:

The shape is a cuboid, which has rectangular faces.

Step 2: Count the faces:

A cuboid has 6 faces, all of which are rectangles.

Step 3: Count the edges:

A cuboid has 12 edges.

Step 4: Count the vertices:

A cuboid has 8 vertices.

Step 5: Verify using Euler’s formula:

Euler’s formula: \( F + V - E = 2 \).

\( 6 + 8 - 12 = 2 \), which holds true.

Step 6: Therefore, a cuboid has 6 faces, 12 edges, and 8 vertices.

Step 1: Identify the shape:

A shape with 2 circular bases and a curved surface is a cylinder.

Step 2: Describe the faces:

A cylinder has 2 flat faces (the circular bases) and 1 curved surface.

Step 3: Describe the edges:

A cylinder has 2 curved edges where the bases meet the curved surface.

Step 4: Describe the vertices:

A cylinder has 0 vertices.

Step 5: Therefore, the shape is a cylinder with 2 circular bases, 1 curved surface, 2 curved edges, and 0 vertices.

Step 1: Identify the shape:

The shape is a cone, which has 1 circular base and 1 curved surface.

Step 2: Understand the net:

The net of a 3D shape is a 2D shape that can be folded to form the 3D shape.

Step 3: Determine the net components:

The curved surface of the cone, when unfolded, forms a sector of a circle.

The base of the cone is a circle.

Step 4: Draw the net:

Draw a sector (a part of a circle) for the curved surface.

Draw a circle for the base, with the radius matching the base of the cone.

Step 5: Therefore, the net of a cone consists of a sector and a circle.

Step 1: Observe the object:

A basketball is a round object used in sports.

Step 2: Match with a 3D shape:

A sphere is a 3D shape that is perfectly round, with all points on the surface equidistant from the center.

Step 3: Describe the properties:

A sphere has 1 curved surface, 0 faces, 0 edges, and 0 vertices.

Step 4: Therefore, the shape of a basketball is a sphere.