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What are the properties (faces, edges, corners, pieces, unbroken edges) of a box based on its net diagram?

Mathematics

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Here are the answers to the questions about the box net:

  1. How many faces does the box have?

    A standard box (rectangular prism) has 6 faces. The net shows 6 main rectangular sections that will form the faces of the box.

    6 faces\boxed{\text{6 faces}}
  2. How many edges do the box have?

    A standard rectangular prism has 12 edges.

    12 edges\boxed{\text{12 edges}}
  3. How many corners does the box have?

    A standard rectangular prism has 8 corners (vertices).

    8 corners\boxed{\text{8 corners}}
  4. Out of how many separate pieces of cardboard was the box made?

    The diagram shows one continuous piece of cardboard that forms the entire net.

    1 piece\boxed{\text{1 piece}}
  5. How many of the edges of the box are unbroken edges?

    "Unbroken edges" refers to the edges of the assembled box that are formed by folding the cardboard along a line (fold lines) rather than by gluing tabs. Counting the fold lines on the net:

    • There are 4 horizontal fold lines in the main body of the net.
    • There are 4 vertical fold lines in the main body of the net.
    • There are 2 fold lines connecting the top and bottom flaps to their respective side faces. Total fold lines = 4+4+2=104 + 4 + 2 = 10. These 10 fold lines become 10 edges of the box. The remaining 2 edges are formed by gluing the tabs.
    10 edges\boxed{\text{10 edges}}
  6. How many tables in total were used to make the box?

    Assuming "tables" is a typo for "tabs" (the small flaps used for gluing the box together):

    • There are 4 tabs along the right side of the main strip of faces.
    • There are 2 tabs on the top flap.
    • There are 2 tabs on the bottom flap. Total tabs = 4+2+2=84 + 2 + 2 = 8.
    8 tabs\boxed{\text{8 tabs}}
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