Cube and Cuboid Formulas, Example Questions
1. In a cube or a cuboid there are six faces in each.
2. In a cube length, breadth and height are same while in cuboid these are different.
3. In a cube the number of unit cubes = and in cuboid the number of unit cube =
Example on Cube and Cuboid
A cube of each side 4 cm, has been painted black, red and green on pairs of opposite faces. It is then cut into small cubes of each side 1 cm.
Then find
1. How many small cubes will be there ?
2. How many small cube will have three faces painted ?
3. How many small cubes will have only two faces painted ?
4. How many small cubes will have only one faces painted ?
5. How many small cubes will have no faces painted ?
6. How many small cubes will have only two faces painted black and green and all other faces unpainted ?
7. How many small cubes will have only two faces painted green and red.
8. How many small cubes will have only two faces painted black and red ?
9. How many small cubes will be only black painted ?
10. How many small cubes will be only red painted ?
11. How many small cubes will be only green painted ?
12. How many small cubes will have atleast one face painted ?
13. How many small cubes will have atleast two faces painted ?
The solution of each question given above, is given below with explanation. Here three faces are visible.
Steps :
(1) A cube of each side 4 cm is here.
(2) It is cut into small cubes of each side of 1 cm.
(3) Opposite faces are painted with black, red and green paints.
1. Total no. of small cubes = 64.
2. No. of small cubes having three faces painted From the figure it is clear that the small cube having three faces coloured are situated at the corners of the big cube because at these corners only three faces of the big cube meet. Therefore the required number of such cubes is always 8, because there are 8 corners.
3. No. of small cubes having only two faces painted From the figure it is clear that to each edge of the big cube 4 small cubes are connected and two out of them are situated at the corners of the big cube which have all the three faces painted. Thus, to each edge two small cubes are left which have two faces painted. As the total no. of edges in a cube are 12, hence the no. of small cubes with two faces coloured
= = 24.
Or
No. of small cubes with two faces coloured
=
Where x =
4. No. of small cubes having only one face painted The cubes which are painted on one face only are the cubes at the centre of each face of the big cube. Since there are 6 faces in the big cube and each of the face of big cube there will be four such small cubes. Hence, in all there will be i.e., 24 such small cubes.
or
5. No. of small cubes having no face painted No. of such small cubes
=
=
6. No. of small cubes having two faces painted black and green There are 4 small cubes in layer II and 4 small cubes in layer III which have two faces painted green and black.
Reqd. no. of such small cubes = 4 + 4 = 8.
7. No. of small cubes having two faces painted green and red.
Reqd. no. of such small cubes = 4 + 4 = 8.
8. No. of small cubes having two faces painted black and red = 4 + 4 = 8.
9. No. of small cubes having only black paint. There will be 8 small cubes which have only black paint. Four cubes will be from one side and 4 from the opposite side.
10. No. of small cubes having only red paint
= 4 + 4 = 8
11. No. of small cubes having only green paint
= 4 + 4 = 8
12. No. of small cubes having atleast one face painted
= No. of small cubes having 1 face painted + 2 faces painted + 3 faces painted
= 24 + 24 +8 = 56
13. No. of small cubes having atleast two faces painted
= No. of small cubes having two faces painted + 3 faces painted
= 24 + 8 = 32
Cube and Cuboid Questions from Previous Year Exams
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Question 1 of 14
1. Question
1 pointsThe following questions are based on the information given below:
1. There is a cuboid whose dimensions are 4 x 3 x 3 cm.
2. The opposite faces of dimensions 4 x 3 are coloured yellow.
3. The opposite faces of other dimensions 4 x 3 are coloured red.
4. The opposite faces of dimensions 3 x 3 are coloured green.
5. Now the cuboid is cut into small cubes of side 1 cm.How many small cubes will have only two faces coloured ?
Correct
Number of small cubes having only two faces coloured = 6 from the front + 6 from the back + 2 from the left + 2 from the right
= 16
Incorrect
Number of small cubes having only two faces coloured = 6 from the front + 6 from the back + 2 from the left + 2 from the right
= 16

Question 2 of 14
2. Question
1 pointsHow many small cubes have three faces coloured ?
Correct
Such cubes are related to the corners of the cuboid and there are 8 corners.
Hence, the required number is 8.
Incorrect
Such cubes are related to the corners of the cuboid and there are 8 corners.
Hence, the required number is 8.

Question 3 of 14
3. Question
1 pointsHow many small cubes will have no face coloured ?
Correct
Number of small cubes have no face coloured = (4  2) x (3  2) = 2 x 1 = 2
Incorrect
Number of small cubes have no face coloured = (4  2) x (3  2) = 2 x 1 = 2

Question 4 of 14
4. Question
1 pointsHow many small cubes will have only one face coloured ?
Correct
Number of small cubes having only one face coloured = 2 x 2 + 2 x 2 + 2 x 1
= 4 + 4 + 2 =10
Incorrect
Number of small cubes having only one face coloured = 2 x 2 + 2 x 2 + 2 x 1
= 4 + 4 + 2 =10

Question 5 of 14
5. Question
1 pointsThe following questions are based on the information given below:
A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
Two faces measuring 4 cm x 1 cm are coloured in black.
Two faces measuring 6 cm x 1 cm are coloured in red.
Two faces measuring 6 cm x 4 cm are coloured in green.
The block is divided into 6 equal cubes of side 1 cm (from 6 cm side), 4 equal cubes of side 1 cm(from 4 cm side).How many cubes having red, green and black colours on at least one side of the cube will be formed ?
Correct
Such cubes are related to the corners of the cuboid. Since the number of corners of the cuboid is 4.Hence, the number of such small cubes is 4.
Incorrect
Such cubes are related to the corners of the cuboid. Since the number of corners of the cuboid is 4.Hence, the number of such small cubes is 4.

Question 6 of 14
6. Question
1 pointsHow many small cubes will be formed ?
Correct
Number of small cubes = l x b x h = 6 x 4 x 1 = 24
Incorrect
Number of small cubes = l x b x h = 6 x 4 x 1 = 24

Question 7 of 14
7. Question
1 pointsHow many cubes will have 4 coloured sides and two noncoloured sides ?
Correct
Only 4 cubes situated at the corners of the cuboid will have 4 coloured and 2 noncoloured sides.
Incorrect
Only 4 cubes situated at the corners of the cuboid will have 4 coloured and 2 noncoloured sides.

Question 8 of 14
8. Question
1 pointsHow many cubes will have green colour on two sides and rest of the four sides having no colour ?
Correct
There are 16 small cubes attached to the outer walls of the cuboid.
Therefore remaining inner small cubes will be the cubes having two sides green coloured.So the required number = 24  16 = 8
Incorrect
There are 16 small cubes attached to the outer walls of the cuboid.
Therefore remaining inner small cubes will be the cubes having two sides green coloured.So the required number = 24  16 = 8

Question 9 of 14
9. Question
1 pointsHow many cubes will remain if the cubes having black and green coloured are removed ?
Correct
Number of small cubes which are Black and Green is 8 in all.
Hence, the number of remaining cubes are = 24  8 = 16
Incorrect
Number of small cubes which are Black and Green is 8 in all.
Hence, the number of remaining cubes are = 24  8 = 16

Question 10 of 14
10. Question
1 pointsThere are 128 cubes with me which are coloured according to two schemes viz.
1. 64 cubes each having two red adjacent faces and one yellow and other blue on their opposite faces while green on the rest.
2. 64 cubes each having two adjacent blue faces and one red and other green on their opposite faces, while red on the rest. They are then mixed up.How many cubes have at least two coloured red faces each ?
Correct
64 and 64 cubes of both types of cubes are such who have at least two coloured faces red each.
Therefore, total number of the required cubes is 128.
Incorrect
64 and 64 cubes of both types of cubes are such who have at least two coloured faces red each.
Therefore, total number of the required cubes is 128.

Question 11 of 14
11. Question
1 pointsWhat is the total number of red faces ?
Correct
No. of red faces among first 64 cubes = 128
No. of red faces among second 64 cubes = 192
Therefore, total number of red faces = 128 + 192 = 320
Incorrect
No. of red faces among first 64 cubes = 128
No. of red faces among second 64 cubes = 192
Therefore, total number of red faces = 128 + 192 = 320

Question 12 of 14
12. Question
1 pointsHow many cubes have two adjacent blue faces each ?
Correct
Second 64 cubes are such each of whose two faces are blue.
Incorrect
Second 64 cubes are such each of whose two faces are blue.

Question 13 of 14
13. Question
1 pointsHow many cubes have only one red face each ?
Correct
Out of 128 cubes no cube have only one face is red
Incorrect
Out of 128 cubes no cube have only one face is red

Question 14 of 14
14. Question
1 pointsWhich two colours have the same number of faces ?
Correct
First 64 cubes are such each of whose two faces are green and second 64 cubes are such each of whose two faces are blue.
Therefore, green and blue colours have the same number of faces.
Incorrect
First 64 cubes are such each of whose two faces are green and second 64 cubes are such each of whose two faces are blue.
Therefore, green and blue colours have the same number of faces.
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Comment made by B.Lkshmi Narasimhan on Nov 5th 2016 at 7:17 am:
this is awesome guys
but I am not able to find the cuboid questions