Identify the correct 2D pattern of the given cuboid:
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Identify the correct 2D pattern of the given cuboid:
Let's go through the options:
A - In this option, we can observe that there are two flaps on the same side.
If we try to turn this net into a box, we should obtain a box where on one side there are two faces one on top of the other while the other side is "open",
meaning this net cannot be turned into a complete and full box.
B - This net looks valid at first glance, but we need to verify that it matches the box we want to draw.
In the original box, we see that we have four flaps of size 9*4, and only two flaps of size 4*4,
if we look at the net we can see that the situation is reversed, there are four flaps of size 4*4 and two flaps of size 9*4,
therefore we can conclude that this net is not suitable.
C - This net at first glance looks valid, it has flaps on both sides so it will close into a box.
Additionally, it matches our drawing - it has four flaps of size 9*4 and two flaps of size 4*4.
Therefore, we can conclude that this net is indeed the correct net.
D - In this net we can see that there are two flaps on the same side, therefore this net will not succeed in becoming a box if we try to create it.
A cuboid is shown below:
What is the surface area of the cuboid?
Look at the original cuboid carefully. The 4×4 faces are the top and bottom, while the four 4×9 faces form the sides. In a correct net, these faces must be arranged so they can fold together.
A net is invalid if it has overlapping faces when folded, missing faces, or wrong face sizes. Also watch for nets where faces would be on the same side - they can't close properly!
No! If two faces extend from the same edge of another face, they'll overlap when you try to fold the net. Each edge can only connect to one other face.
Use the fold test: Imagine folding each face up. Can you close all 6 faces into a complete box without gaps or overlaps? If yes, it's correct!
The dimensions tell you exactly how many faces of each size you need. A 4×4×9 cuboid needs 2 faces that are 4×4 and 4 faces that are 4×9. Count these in each net option!
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