Directions: In the following questions,certain information regarding cubes are given on the basis of which you need to select the best option. You can also review your choices by clicking into answer section.
5. The following questions are based on the information given below:
A cube of 3cm*3cm*3cm is kept in the corner of a room and painted in three different colours, each face in one colour. The cube is then cut into equal cubes of side 1 cm.
I. How many smaller cubes are formed?
A. 33
B. 9
C. 27
D. 30
Answer
Explanation:
No. of cubes = Volume of larger cube/Volume of smaller cube
= (3*3*3)/(1*1*1)
= 27
II. How many cubes have exactly one face painted?
A. 12
B. 11
C. 16
D. 15
Answer
Explanation:
The cube has been painted on the three visible faces. The three faces are adjacent.
No. of cubes painted on 1 face = (3*2*2)
Cubes on the 3 visible faces = 4*3 = 12
III. How many cubes have three faces painted?
A. 3
B. 8
C. 2
D. 1
Answer
Explanation:
The cube at the corner connecting the 3 visible faces is painted on 3 faces.
IV. How many cubes are unpainted on all faces?
A. 8
B. 7
C. 1
D. 9
Answer
Explanation:
The cube at the center of the larger cube, the 3 cube at the center of the 3 invisible faces, the 3 cube at the center of the 3 edges connecting the invisible faces and the cube at the corner joining the invisible faces are unpainted on all sides. For cubes painted on 3 adjacent faces,
No. of cubes unpainted on all sides = (n-1)³ Here, n=3
So, the answer is 8.
V. How many cubes are coloured on at most 1 face?
A. 275
B. 218
C. 216
D. 210
Answer
Explanation:
No. of cubes painted on at most 1 face
= No. of cubes unpainted on all faces+ No. of cubes painted on only 1 face
= (n-2)³+6(n-2)²
= 125+150
= 275
VI. How many cubes are painted only on 2 faces?
A. 68
B. 70
C. 60
D. 25
Answer
Explanation:
12(n-2) = 60
VII. How many cubes are uncoloured on all faces?
A. 125
B. 150
C. 216
D. 196
Answer
Explanation:
(n-2)³ = 125
VIII. How many cubes have at least two faces painted?
A. 8
B. 49
C. 60
D. 68
Answer
Explanation:
12(n-2)+8 = 68
6. The following questions are based on the information given below:
All the opposite faces of a big cube are coloured with red, black and green colours. After that is cut into 64 small equal cubes.
I. How many small cubes are there where one face is green and other one is either black or red?
A. 28
B. 8
C. 16
D. 24
Answer
Explanation:
Number of small cubes having one face green and the other one is either red or black
= 8 x 2 = 16 
II. How many small cubes are there whose no faces are coloured?
A.0
B.4
C.8
D.16
Answer
Explanation:
Number of small cubes having no face coloured
= (x – 2)3
= (4 – 2)3
= 8
III. How many small cubes are there whose 3 faces are coloured ?
A. 4
B. 8
C. 16
D. 24
Answer
Explanation:
Number of small cubes having three faces coloured
= 1 at each corner
= 1 x 8
= 8
IV. How many small cubes are there whose only one face is coloured?
A.32
B.8
C.16
D.24
Answer
Explanation:
Number of small cubes having only one face coloured
= 4 from each face
= 4 x 6
= 24
V. How many small cubes are there whose at the most two faces are coloured ?
A. 48
B. 56
C. 28
D. 24
Answer
Explanation:
Number of small cubes having two faces coloured = 8 + 8 + 4 + 4 = 24
Number of small cubes having only one face coloured = 4 x 6 = 24
Number of small cubes having no face coloured = 4 + 4 = 8
Therefore, total number of small cubes whose at the most two faces are coloured
= 24 + 24 + 8 = 56.
7. A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on 3 faces?
A. 12
B. 16
C. 6
D. 8
Answer
Explanation:
The cubes at the corners of the bigger cube will be painted on 3 sides.
There are 8 corners. 8 cubes are painted on 3 sides.
