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Use the 3D sketch and the given specifications to fill in all the missing dimensions of the edges of the net.
Mathematics
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Step-by-step solution
2 stepsTo fill in the missing dimensions on the net, we first identify the dimensions of the 3D cuboid shown. Let's define:
- : The length of the cuboid (the longer dimension of the base).
- : The width of the cuboid (the shorter dimension of the base).
- : The height of the cuboid.
Identify the dimensions of the main faces on the net.
The central large rectangle on the net represents one of the main faces (e.g., the bottom).
- The horizontal arrow above the central rectangle indicates its width, which corresponds to .
- The vertical arrow to the left of the central rectangle indicates its length, which corresponds to . So, the central rectangle is .
The faces attached to the central rectangle are the side faces.
- The rectangles directly above and below the central rectangle have a width of and a height of .
- The rectangles to the left and right of the central rectangle have a length of and a height of .
- The topmost rectangle, attached to the face, is the top face, with dimensions .
Determine the dimensions for the numbered flaps (1, 2, 3, 4).
These flaps are designed to fold and glue to corresponding edges when the net is assembled into a cuboid. Their lengths must match the edges they attach to.
- 1. This flap is attached to the top edge of the topmost rectangle (the top face, ). The length of this edge is .
- 2. This flap is attached to the bottom edge of the rectangle below the central rectangle (a side face, ). The length of this edge is .
- 3. This flap is attached to the left edge of the rectangle to the left of the central rectangle (a side face, ). The length of this edge is .
- 4. This flap is attached to the right edge of the rectangle to the right of the central rectangle (a side face, ). The length of this edge is .
The missing dimensions are:
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