Question

practice representing a three - dimensional figure with a net
study the example showing how to draw a net for a three - dimensional figure. then solve problems 1–5.
example
an artist needs a sheet of copper that can be bent to form a cube. draw a net the artist can use to make the cube.
imagine cutting a cube apart along some of the edges and unfolding it.
images of cube, unfolding, net
this net is one possible net for a cube.

1. a. what shapes are in any net for a cube? explain.

b. you could cut the cube in the example along other edges to make a net with a different arrangement of squares. draw an example of another net for a cube.

1. hai says that every net for a prism is made up of exactly six faces. explain why hai’s statement is incorrect.

Explanation:

1a

A cube has 6 square faces, all equal. When unfolded into a net, these faces remain squares. So any net for a cube consists of squares because each face of the cube is a square, and the net is just the unfolded faces.

One common net for a cube (other than the cross - shaped one) is the "2 - 3 - 1" arrangement or the "L - shaped" extension. For example, we can have three squares in a row, with one square attached to the top of the first square in the row, one square attached to the top of the second square in the row, and one square attached to the bottom of the third square in the row. (Since it's a drawing - based answer, we can describe the structure: Draw three squares horizontally adjacent. Then draw one square above the first square, one square above the second square, and one square below the third square. When folded, this will form a cube.)

A prism is defined by its two congruent polygonal bases and rectangular (or other parallelogram - shaped) lateral faces. The number of faces of a prism is given by the formula \(F=n + 2\), where \(n\) is the number of sides of the polygonal base. For a triangular prism (\(n = 3\)), the number of faces is \(3+2=5\) (2 triangular bases and 3 rectangular lateral faces). So not all prisms have 6 faces. Hai's statement is incorrect because prisms with bases that are not quadrilaterals (e.g., triangular prisms) have fewer than 6 faces.

Answer:

The shapes in any net for a cube are squares. A cube has 6 congruent square faces, and a net is the 2 - D representation of the unfolded 3 - D cube, so it is made up of these 6 square faces.

1b