# what is the maximum possible number of cuts required to cut a cube into 216 identical pieces?

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## What is the minimum number of cuts required to cut a cube into 216 identical pieces?

Fifteen cuts in total. The cube-root of 216 is 6 - therefore you need five cuts per axis.

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## What is the minimum number of cuts required to cut a cube into 216 identical pieces?

Wiki User ∙ 7y ago Best Answer Copy

Fifteen cuts in total. The cube-root of 216 is 6 - therefore you need five cuts per axis.

Wiki User ∙ 7y ago This answer is: Study guides Algebra 20 cards

A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common f...

The sum or difference of p and q is the of the x-term in the trinomial

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If you do not re-stack the pieces, then 15 cuts.

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People also asked

## A cube is cut into 216 identical smaller cubes. In how many different ways can the smaller cubes be arranged to form cuboids of different surface areas if no two cubes are to be placed one above another?

Answer (1 of 2): The question is basically asking you how many factors of 216 there are. 216= (2^3)*(3^3) Therefore cuboids can be formed measuring: 1*216 2*108 3*72 4*54 6*36 8*27 9*24 12*18 The answer is 8.

A cube is cut into 216 identical smaller cubes. In how many different ways can the smaller cubes be arranged to form cuboids of different surface areas if no two cubes are to be placed one above another?

Sort Saiket Talukdar

Former Analyst at The Smart Cube (2017–2018)Author has 53 answers and 62.7K answer views6y

i think the answer will be 8.

since no cube can be paced on top of each other hence the height of the resulting cuboid will always be 1.

hence immediately the first arrangement that comes to mind is horizontal line of 216 cubes.

if that is true then another arrangement can be two lines of 108 cubes each.

it actually boils down to finding the total no of ways 216 can be factored . which comes to 16.

now consider a the case of 2 lines with 108 cubes each and 108 lines with 2 cubes each.both are exactly the same arrangements with just a different perspective of looking at it( think horizontal to ve

Related questions

Each of 216 small identical cubes are painted blue on all faces and all these cubes are arranged to form a large cube. Now all the faces of large cubes are painted pink. How many small cubes have exactly two faces painted pink?

A cube is cut into 216 identical smaller cubes. In how many different ways can the smaller cubes be arranged to form cuboids of different surface area if no two cubes are to be placed one above another?

A cube is coloured red on all faces. It is cut into 216 smaller cubes of equal size. How many cubes have two faces coloured?

A cube is painted teal on 3 of its faces, blue on 2 of its faces and red on 1 of its faces. The cube is now cut into 216 smaller and identical cubes. How many smaller cubes are painted with exactly two different colors?

Three different faces of a cube are painted in three different colours–red, green and blue. This cube is now cut into 216 smaller but identical cubes. What are the least and the largest numbers of small cubes that have exactly one face painted?

Joel Reynolds Corless

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The question is basically asking you how many factors of 216 there are.

216= (2^3)*(3^3)

Therefore cuboids can be formed measuring:

1*216 2*108 3*72 4*54 6*36 8*27 9*24 12*18 The answer is 8. Ritika Khurana 3y Related

A cube is painted with red colour on its five faces. If this cube is cut into 216 equal small cubes, how many small cubes will have no faces coloured?

Going by the question, since there are 216 smaller cubes it means there are

6 x 6 cubes on each side. Here is how it will look like.

Assume the front face is not painted red and every other face is. Now you want the number of cubes with no side painted. For this imagine peeling off the top layer, bottom one, left right and back one.

Top layer has cubes = 36

Bottom layer = 36

Left layer = 24 (not 36 because its top 6 and bottom 6 are already gone in previous steps)

Right layer = 24

Back layer = 16 (again this has its top, bottom, left and right already gone, leaving you with a 4 x 4 block)

Remaining cu Khadija Abba

Worked at Spirit of MathAuthor has 58 answers and 296.7K answer views4y

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Two opposite faces of a cube are painted red and it is then cut into 64 smaller but identical cubes. How many smaller cubes are not painted at all?

It should be noted that because the cube was painted on opposite sides, the below is correct. If the cube had paint on adjacent sides, a slightly different approach would have to be taken.

Aaron Jantzen

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Any Japanese chef can give you a far better answer to this than your typical mathematician will. A mathematician might tell you 12 or 16 depending upon whether they rearrange the pieces before cutting. However a Japanese chef will tell you “thousands” and that is meant literally. Not only can it be done, it is indeed regularly done by these chefs. The secret is called the Katsuramuki technique. Quite simply, the first cut is a spiral, which is normally done by hand with a sharp knife on a log-shaped vegetable such as Daikon, resulting in a long sheet, but could work with a cube by gradually ro

Aditya

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

Click here👆to get an answer to your question ✍️ Find the least number of cuts required which can cut a cube into 60 identical pieces?

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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