what is the least possible number of cuts required to cut a cube into 70 identical pieces?

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Find the least number of cuts required which can cut a cube into 60 identical pieces?

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Question

Find the least number of cuts required which can cut a cube into 60 identical pieces?

A

9

B

12

C

15

D

5

Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is A)

We need to cut a ute to 60 identical pieces

If we cut oru it become 2 identical pieces.

If we cut twice on same face it becomes 3 identical pieces.

If we cute once on one face and another on other face it becomes 4 identical pieces.

∴ general formula ⇒ number of identical pieces=(l+1)(m+1)(n+1)

(n,m,l)= no. of cut on each face

Given:- (l+1)(m+1)(n+1)=60

(l+1)(m+1)(n+1)=3×4×5

⇒(l+1)=3,m+1=4,n+1=5

⇒l=2,m=3,n=4

∴ total no. of cuts =l+m+n=3+4+2

=9

∴ minimum 9 cuts have to be made to get 60 identical pieces.

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What is the least possible number of cuts required to cut a cube into 150 identical pieces

According to the question We have to find the least possible number of cuts so the total count of pieces got withxy and z axis are X1xY1xZ141x41x51 Thus the total no of cuts are5x5x6150 Least no of possible cuts are 44513 Hence this is the final answer

General Studies for Civil Services Preliminary Examinations : CSAT ( GS Paper II )>Cubes and Dices>Practice Exercises>Q 20

EASY

Civil Services Preliminary Examination Paper 2

IMPORTANT Earn 100

What is the least possible number of cuts required to cut a cube into

150 identical pieces? 50%

students answered this correctly

Important Questions on Cubes and Dices

EASY

Civil Services Preliminary Examination Paper 2

IMPORTANT

General Studies for Civil Services Preliminary Examinations : CSAT ( GS Paper II )>Non-Verbal Reasoning>Exercise>Q 1

Directions for Questions: There is a relation between figures A and B. Choose a similar relationship between C and D by choosing a suitable figure D from the answer set.

Problem Figures Answer figure EASY

Civil Services Preliminary Examination Paper 2

IMPORTANT

General Studies for Civil Services Preliminary Examinations : CSAT ( GS Paper II )>Non-Verbal Reasoning>Exercise>Q 4

Directions for Questions: There is a relationship between A and B of the problem figures. Establish a similar relationship between C and D by selecting a suitable figure from the Answer Set.

Problem Figures

Answer Figures

EASY

Civil Services Preliminary Examination Paper 2

IMPORTANT

General Studies for Civil Services Preliminary Examinations : CSAT ( GS Paper II )>Non-Verbal Reasoning>Exercise>Q 5

Directions for Questions: There is a relationship between A and B of the problem figures. Establish a similar relationship between C and D by selecting a suitable figure from the Answer Set.

Problem Figures

Answer Figures

Important Points to Remember on Cubes and Dices

Cubes and Dice1. On a die, the sum of the number on the opposite faces will always be equal to ‘

7 ’. The number 1 will be opposite to 6, 2 is opposite to 5 and 3 is opposite to 4 .

2. If one of the numbers is common in both the dice when two dice have the same surface, then the remaining surfaces of both the dice are opposite to each other.3. If only one element is common on both the dice but at a different position, then rotate the dice in a clockwise direction using the common side to get the opposite surface.

4. Here, the clockwise pattern is

265 and 241 . Hence, 6 is opposite to 4 and 5 is opposite to 1 . Thus, 4 is opposite to 2 .

5. There are three different types of open die:6. Here,

1 is opposite to 5. 2 is opposite to 4. 3 is opposite to 6 .

7. Here,

1 is opposite to 6. 2 is opposite to 4. 3 is opposite to 5 .

8. Here,

1 is opposite to 3. 2 is opposite to 5. 6 is opposite to 4 .

Points to remember about cubes:

i. A cube has 6 faces, 12 edges and 8 vertices.

ii. For n cuts mutually parallel to the base (or any other face), we get

n+1 solid pieces.

iii. On painting the outer surface of a cube with the same colour:

(a) Number of cubes with

3 faces painted = 8

(b)  Number of cubes with exactly 2 faces painted

=(n-2)× (number of edges)

(c)  Number of cubes with exactly 1 face painted

=(n-2)2×6

(d) Number of cubes with 0 faces painted black

=(n-2)3=8

Questions featured in Previous Year Papers on Cubes and Dices

EASY PREVIOUS YEAR

Civil Services Preliminary Examination Paper 2

IMPORTANT

General Studies for Civil Services Preliminary Examinations : CSAT ( GS Paper II )>Cubes and Dices>Practice Exercises>Q 12

A dice is thrown four times and its four different positions are shown below. Find the number on the face opposite the face showing

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What is the least number of cuts required to cut a cube into 84 identical pieces,

What is the least number of cuts required to cut a cube into 84 identical pieces, assuming all cuts are made ... faces of the cube? 11 12 13 10

What is the least number of cuts required to cut a cube into 84 identical pieces,

asked in Quantitative Aptitude Aug 22, 2015

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