CUBE &
CUBOID CUTTING in Reasoning section are mandatory part covers 515 questions of
SSC IBPS or other competitive exams. Such questions are very easy to solve
within 35 seconds by using IMPORTANT FORMULA TABLE.
IMPORTANT
FORMULA TABLE to solve not only provides accurate solution but also helps in
achieving maximum score in any competitive exam.
Aspirants
are recommended to use IMPORTANT FORMULAE TABLE to solve CUBE & CUBOID CUTTING
in Reasoning section to get maximum score in exam.
IMPORTANT FORMULAE FOR CUBE &
CUBOID CUTTING:
Let the
statement is given as follows:
A cube has ‘N’ cm side painted with
red color on the faces. Now it is cut into small cubes of ‘n’ cm side.
Read the
statement carefully line by line and solve the question by using IMPORTANT
FORMULAE provided in below Table.
S. No.

NO. OF QUESTIONS

IMPORTANT FORMULA TABLE

1

No. of
Small Cubes cut from Big Cube

(N / n)^{3}

2

Total Small Cubes Which have only NO FACE PAINTED

[(N/n) – 2]^{3}

3

Total Small Cubes Which have only ONE FACE PAINTED

[Count on One Face x 6] / 1^{}

4

Total Small Cubes Which have only TWO FACES PAINTED

[Count on Two
Face x 6] / 2^{}

5

Total Small Cubes Which have only THREE FACES PAINTED

[Count on Three Face x 6] / 3^{}

Count the faces after cutting for
face one, two or three See example for clarity.
Question
1:
A cube has ‘5’
cm side painted with red color on the faces. Now it is cut into small cubes of ‘1’
cm side. Answers the following:
1. How many
small cubes cut from the big cube?
2. How many
small cubes which have NO face painted?
3. How many
total small cubes whose have only one face painted?
4. How many
small cubes which have only two faces painted?
5. How many
small cubes which have only three faces painted?
6. How many small
cubes which have at least one face painted?
7. How many
small cubes which have at most two faces painted?
Solution:
From the above statement, N = 5 & n = 1
Now cut the one face of cube, it will
appear same as shown in Figure 1 (above).
Then Count on the face for ONE, TWO &
THREE same as shown in Figure 2 (above).
Use the FORMULA Table for Solution:
S. No.

QUESTIONS

IMPORTANT FORMULA TABLE

1

No. of
Small Cubes cut from Big Cube

(5 / 1)^{3} = 125

2

Total Small Cubes Which have only NO FACE PAINTED (0)

[(5/1) – 2]^{3}=
[3]^{3}_{ }= 27

3

Total Small Cubes Which have only ONE FACE PAINTED (1)

[9 x 6] / 1 = 54^{}

4

Total Small Cubes Which have only TWO FACES PAINTED (2)

[12 x 6] / 2 =
36^{}

5

Total Small Cubes Which have only THREE FACES PAINTED (3)

[4 x 6] / 3 = 8^{}

6

Total Small Cubes Which have at least ONE FACE PAINTED

(1) + (2) +
(3) =54+36+8=98^{}

7

Total Small Cubes Which have at most TWO FACES PAINTED

(0) + (1) + (2) = 27+54+36=117^{}

Do the practices for different sizes of
cubes cut into different no. of small cubes from previous papers set to achieve
cutoff score in SSC IBPS or other competitive exams.
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