# 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 Dice**

**1.**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

## 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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## 2 Answers

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