# Cube and Cuboid Questions​ ## Definition of Cube and Cuboid

A cube is a shape having three dimensions and 6 faces, 12 edges, and 8 corners. In a cube all the edges are of similar kind and include square-shaped faces. A Cube, which is a three-dimensional dense image have the same measurements of all of its dimensions. In total, there are 6 faces, 8 vertices & 12 edges in a cube. Vertex denotes the corners and an edge denotes the side.
These dimensions are known as length, breadth, and height. Conversely if a cube has six rectangular faces then, it is known as a cuboid. Each face of the cuboid is in rectangular shape, and at least four rectangles among them are identical.
The most important thing to consider while solving the questions of such types is to visualizing the cube in your mind. By looking at the cube you can clearly identify the basic terminologies such as the face, vertex, and edge of a cube. Each line segment in the cuboid is edge, and the points where the edges meet is vertex. All edges are the sides, and vertices are the corners of the cuboid, and the opposite faces are parallel rectangles, which include similar dimensions.

### Rules

• When a cube have its side measuring unit as ‘a’ and is painted on every face, and then it is reduced into smaller parts with measuring unit of sides as ‘b.’ Then you are expected to answer the quantity of cubes with ‘n’ faces painted. Reasonably if you see one specific edge of any big cube and visualize the smaller parts of that by making a/b, then the number of smaller cubes will be calculated by (a/b)^3.
• As we know that all the reduced cube parts will always have at least one face in the inner side, which means not on the exterior side; therefore, all the reduced cubes will have faces that are not painted. Also as the larger cubes meet at the corner points, i.e. 3, hence, the lesser cubes will be having a limit of 3 painted faces. Therefore, the smaller cubes with 3 faces painted = Number of large cube’s corners = every time 8 cubes. The only condition is that all the faces of the larger cubes are painted.
• To get the total number of smaller cubes having 2 faces painted only, we need to check the cube edges points. These are the points where 2 faces of the larger cubes meet. To solve these questions, you always need to include the corner cubes also, hence if you will remove 2 cubes from the total number of cubes on each edge, then you will easily get the answer.
• The cubes with one face painted can only be at the cubes at the face of the bigger cubes.

Question 1 Time: 00:00:00
The following questions (1-5) are based on the information given below:

A cuboid shaped wooden block has 8 cm length, 4 cm breadth and 1 cm height.
Two faces measuring 4 cm x 1 cm are coloured in black.
Two faces measuring 8 cm x 1 cm are coloured in yellow.
Two faces measuring 8 cm x 4 cm are coloured in purple.
The block is divided into 8 equal cubes of side 1 cm (from 8 cm side), 4 equal cubes of side 1 cm(from 4 cm side).

How many cubes having yellow, purple and black colors on at least one side of the cube will be formed? 16

16

12

12

10

10

4

4

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Question 2 Time: 00:00:00
A cuboid shaped wooden block has 8 cm length, 4 cm breadth and 1 cm height.
Two faces measuring 4 cm x 1 cm are coloured in black.
Two faces measuring 8 cm x 1 cm are coloured in yellow.
Two faces measuring 8 cm x 4 cm are coloured in purple.
The block is divided into 8 equal cubes of side 1 cm (from 8 cm side), 4 equal cubes of side 1 cm(from 4 cm side).

How many small cubes will be formed? 8

8

12

12

16

16

32

32

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Question 3 Time: 00:00:00
A cuboid shaped wooden block has 8 cm length, 4 cm breadth and 1 cm height.
Two faces measuring 4 cm x 1 cm are coloured in black.
Two faces measuring 8 cm x 1 cm are coloured in yellow.
Two faces measuring 8 cm x 4 cm are coloured in purple.
The block is divided into 8 equal cubes of side 1 cm (from 8 cm side), 4 equal cubes of side 1 cm(from 4 cm side).

How many cubes will have 4 colored sides and two non-colored sides? 8

8

4

4

16

16

10

10

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Question 4 Time: 00:00:00
A cuboid shaped wooden block has 8 cm length, 4 cm breadth and 1 cm height.
Two faces measuring 4 cm x 1 cm are coloured in black.
Two faces measuring 8 cm x 1 cm are coloured in yellow.
Two faces measuring 8 cm x 4 cm are coloured in purple.
The block is divided into 8 equal cubes of side 1 cm (from 8 cm side), 4 equal cubes of side 1 cm(from 4 cm side).

How many cubes will have Purple color on two sides and rest of the four sides having no color? 12

12

10

10

8

8

4

4

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Question 5 Time: 00:00:00
A cuboid shaped wooden block has 8 cm length, 4 cm breadth and 1 cm height.
Two faces measuring 4 cm x 1 cm are coloured in black.
Two faces measuring 8 cm x 1 cm are coloured in yellow.
Two faces measuring 8 cm x 4 cm are coloured in purple.
The block is divided into 8 equal cubes of side 1 cm (from 8 cm side), 4 equal cubes of side 1 cm(from 4 cm side).

How many cubes will remain if the cubes having black and purple colored are removed? 4

4

8

8

16

16

24

24

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Question 6 Time: 00:00:00
The following questions (6-10) are based on the information given below:

There is a cuboid whose dimensions are 6 x 3 x 3 cm.
The opposite faces of dimensions 6 x 3 are colored yellow.
The opposite faces of other dimensions 6 x 3 are colored red.
The opposite faces of dimensions 3 x 3 are colored green.
Now the cuboid is cut into small cubes of side 1 cm.

How many small cubes will have only two faces colored? 12

12

24

24

16

16

12

12

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Question 7 Time: 00:00:00
There is a cuboid whose dimensions are 6 x 3 x 3 cm.
The opposite faces of dimensions 6 x 3 are colored yellow.
The opposite faces of other dimensions 6 x 3 are colored red.
The opposite faces of dimensions 3 x 3 are colored green.
Now the cuboid is cut into small cubes of side 1 cm.

How many small cubes have three faces colored? 24

24

20

20

16

16

8

8

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Question 8 Time: 00:00:00
There is a cuboid whose dimensions are 6 x 3 x 3 cm.
The opposite faces of dimensions 6 x 3 are colored yellow.
The opposite faces of other dimensions 6 x 3 are colored red.
The opposite faces of dimensions 3 x 3 are colored green.
Now the cuboid is cut into small cubes of side 1 cm.

How many small cubes will have no face colored? 1

1

2

2

4

4

8

8

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Question 9 Time: 00:00:00
There is a cuboid whose dimensions are 6 x 3 x 3 cm.
The opposite faces of dimensions 6 x 3 are colored yellow.
The opposite faces of other dimensions 6 x 3 are colored red.
The opposite faces of dimensions 3 x 3 are colored green.
Now the cuboid is cut into small cubes of side 1 cm.

How many small cubes will have only one face colored? 10

10

12

12

14

14

18

18

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Question 10 Time: 00:00:00
There is a cuboid whose dimensions are 6 x 3 x 3 cm.
The opposite faces of dimensions 6 x 3 are colored yellow.
The opposite faces of other dimensions 6 x 3 are colored red.
The opposite faces of dimensions 3 x 3 are colored green.
Now the cuboid is cut into small cubes of side 1 cm.

Two cubes, each of edge 20 cm, are joined to form single cuboid. What is the surface area of the new cuboid so formed? 2000 cms

2000 cms

4000 cms

4000 cms

2400 cms

2400 cms

6000 cms

6000 cms

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Question 11 Time: 00:00:00
A cube of 2.7 liters volume will have each edge closest to 18 cm

18 cm

24 cm

24 cm

14 cm

14 cm

36 cm

36 cm