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Nets of cuboids
Trace a line around the faces of a cuboid while rolling it on its faces. The resulting plane figure is the net of the cuboid.
By cutting certain edges, a cuboid can be unfolded into a plane figure. This is also the net of the cuboid.
Additional Material
How many edges of a cuboid should be cut to form a plane figure when unfolded? Mark the edges that should be cut with different colours.
In the net, the \latex{ 6 } faces are held together by \latex{ 5 } edges.
To unfold a cuboid, \latex{12 - 5 = 7} edges must be cut.
To unfold a cuboid, \latex{12 - 5 = 7} edges must be cut.
Example
A cube has a letter on each face, and the same letter can occur more than once. The figures show the cube after three throws. What letter is on the bottom of the cube after each throw?
Solution
Draw the possible positions of the \latex{ 3 } faces visible after the first two throws.
Based on the third throw, try to assemble them into a net. If the two S-s were on top of each other, you would not be able to fold them into a cube, so the two S-s are different. Based on the relative positions of A and R, the following is the only net you can make.
Based on the net, you can see that, after the first throw, the letter S, found opposite to A, is on the bottom of the cube. After the second throw, the letter S on top is the one adjacent to O, so the letter A is on the opposite side. Since there is only one letter A, letter S is on the bottom after the third throw.
Exercises
{{exercise_number}}. Draw as many nets of a cube as you can with edges measuring \latex{ 1 } \latex{ cm } in length.
{{exercise_number}}. Roll a die on your notebook to get the net shown in the image when tracing a line around its faces. Write the number of dots on the bottom face in the squares. (→)
{{exercise_number}}. Draw the nets you get when unfolding the cubes along the colourful edges. Mark the adjacent faces with the same colour as the corresponding edges. (→)
a)
b)
{{exercise_number}}. You have to fold the red net into a cube. To do so, you must use one of the \latex{ 10 } squares marked by letters. Which square is needed to complement the red figure? Find all the solutions. (→)
B
C
D
E
A
F
G
H
I
J
{{exercise_number}}. What letter will be on the face opposite X when folding the nets into cubes?
a)
b)
c)
d)
X
L
A
U
R
A
U
X
S
S
N
A
X
N
A
I
R
B
C
H
R
I
S
X
{{exercise_number}}. The net of the cube has a number on each face. Write the sum of the numbers meeting at a vertex on the given vertex. What is the largest number written on a vertex? (→)
a)
b)
\latex{ 1 }
\latex{ 4 }
\latex{ 0 }
\latex{ 3 }
\latex{ 2 }
\latex{ 6 }
\latex{ 2 }
\latex{ 8 }
\latex{ 9 }
\latex{ 5 }
\latex{ 7 }
\latex{ 10 }
{{exercise_number}}. Which of the following nets can be folded into a standard die?
\latex{ A })
\latex{ B })
\latex{ C })
{{exercise_number}}. Draw the net of the cuboid whose edges meeting at a vertex are
a) \latex{ 1 } \latex{ cm }; \latex{ 2 } \latex{ cm }; \latex{ 3 } \latex{ cm };
b) \latex{ 2 } \latex{ cm }; \latex{ 2 } \latex{ cm }; \latex{ 3 } \latex{ cm };
c) \latex{ 8 } \latex{ mm }; \latex{ 10 } \latex{ mm }; \latex{ 15 } \latex{ mm };
d) \latex{ 20 } \latex{ mm }; \latex{ 10 } \latex{ mm }; \latex{ 4 } \latex{ cm }.
{{exercise_number}}. A letter is written on each face of a cube. The relative position and direction of the letters are fixed. The image shows the results of three throws. (→)
Make the net of a cube from paper and write the letters on it. Fold it into a cube and check to make sure all the letters are in the correct positions.
{{exercise_number}}. The cuboid in the image consists of unit cubes.
a) How many unit cubes does it consist of?
b) How many unit squares border the cuboid?
c) Which of the following nets can be the net of the cuboid?
b) How many unit squares border the cuboid?
c) Which of the following nets can be the net of the cuboid?
A)
B)
C)
{{exercise_number}}. The edges of a cuboid are
\latex{ 3 } \latex{ cm }, \latex{ 4 } \latex{ cm } and \latex{ 5 } \latex{ cm } long. When cutting the cuboid along the edges, you get the nets shown in the image. How many \latex{ centimetres } did you have to cut in each case? Make the nets and glue them together to form cuboids. (→)
\latex{ 3 }
\latex{ 3 }
\latex{ 3 }
\latex{ 3 }
\latex{ 3 }
\latex{ 3 }
\latex{ 3 }
\latex{ 3 }
\latex{ 4 }
\latex{ 4 }
\latex{ 4 }
\latex{ 5 }
\latex{ 5 }
a)
b)
\latex{ 4 }
{{exercise_number}}. Which net belongs to which solid?
A)
B)
C)
D)
\latex{ I. }
\latex{ II. }
\latex{ III. }
\latex{ IV. }
{{exercise_number}}. You can see the nets of the cuboids in the images. Which net belongs to which cuboid? Based on the numbers, calculate the sum of the rectangles' area in each case.
A)
B)
\latex{ I. }
\latex{ II. }
\latex{ 3 }
\latex{ 3 }
\latex{ 5 }
\latex{ 3 }
\latex{ 5 }
\latex{ 3 }
\latex{ 6 }
\latex{ 4 }
\latex{ 4 }
\latex{ 4 }
\latex{ 4 }
\latex{ 4 }
\latex{ 4 }
\latex{ 8 }
{{exercise_number}}. One of the faces of a cuboid is the rectangle shown in the image. The cuboid has a
\latex{ 1 } \latex{ cm } long edge. How long are the edges? Draw the net of the cuboid. (→)
\latex{ 4 }
\latex{ 7 }
{{exercise_number}}. The image shows two views of a cuboid. How long are the edges? Draw the net of the cuboid and its top view. (→)
\latex{ 6 }
\latex{ 5 }
\latex{ 6 }
\latex{ 3 }
Quiz
Which net does not belong to the cube shown in the image?
A)
B)
C)
D)
