# Cube and Cuboid Questions and Answers

## Questions and Answers for Cube and Cuboid

This page contains Cube and Cuboid Questions and Answers. 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. In total, there are 6 faces, 8 vertices & 12 edges in a cube. Vertex denotes the corners and an edge denotes the side. ### Introduction of Cubes and Cuboids

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 of Cube and Cuboid

• 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 $\frac{a}{b}$ then the number of smaller cubes will be calculated by $(\frac{a}{b})^3$
• 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.

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### Cube and Cuboid Questions​ and Answers

1. 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

36.36%

12

12

18.18%

10

10

18.18%

4

4

27.27%

In this type of questions these cubes are related to the corners of the cuboid. Since the number of corners of the cuboid is 4, the answer is 4. 2. 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

11.11%

12

12

22.22%

16

16

27.78%

32

32

38.89%

In case of cuboids the Number of small cubes is always calculated as = l x b x h = 8 x 4 x 1 = 32 3. 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

23.53%

4

4

64.71%

16

16

5.88%

10

10

5.88%

When all the sides of a cuboid are colored, all the 4 cubes situated at the corners of the cuboid will have 4 colored and 2 non-colored sides. 4. 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

28.57%

10

10

14.29%

8

8

28.57%

4

4

28.57%

There are 20 small cubes attached to the outer walls of the cuboid.
Therefore remaining inner small cubes will be the cubes having two sides with black color.
So the required number is total cubes minus outside cubes= 32 - 20 = 12. 5. 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

33.33%

8

8

16.67%

16

16

16.67%

24

24

33.33%

Number of small cubes which are Black and purple is 8 in all. So, the number of remaining cubes is total cubes minus cubes with black and purple color - 32 - 8 = 24 6. 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

54.55%

24

24

27.27%

16

16

9.09%

10

10

9.09%

Here when the cuboid is divided into small cubes of 1cm, The number of small cubes having only two faces coloured = 10 from the front + 10 from the back + 2 from the left + 2 from the right. 10+10+2+2 = 24. 7. 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

11.11%

20

20

11.11%

16

16

11.11%

8

8

66.67%

Here the rule of cube applies. All eight corners of the cuboid can only have 3 fares colored. Hence, the required number is 8. 8. 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

20%

2

2

10%

4

4

40%

8

8

30%

Number of small cubes that have no face colored would be the internal cube.

To calculate the same  = (6 - 2) x (3 - 2) x (3 - 2) = 4 x 1 x 1 = 4 9. 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

20%

12

12

40%

14

14

10%

18

18

30%

Here only the 4 internal cubes of 4 sides measuring 6 cms and 2 cubes of sides measuring 3 cms would have only 1 side painted. Hence, Number of small cubes having only one face colored would be 4 x 2 + 4 x 2 + 2 x 1 = 18 cubes. 10. 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 $cm^{2}$

2000 $cm^{2}$

20%

4000 $cm^{2}$

4000 $cm^{2}$

50%

2400 $cm^{2}$

2400 $cm^{2}$

20%

6000 $cm^{2}$

6000 $cm^{2}$

10%

Here length of cuboid = 40 cm.
So the breadth and height of cuboid would be = 20 cm.
To calculate the surface area of the thus formed cuboid is = 2(L x B + B x H + H x L)
surface area = 2(40 x 20 + 20 x 20 + 40 x 20) = 4000 $cm^{2}$  ×