what is the least possible number of cuts required to cut a cube into 729 identical pieces?

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How many minimum number of cuts are required if a cube of volume 729 cubic units is to be cut into unit cubes?

How many minimum number of cuts are required if a cube of volume 729 cubic units is to be cut into unit cubes?

Byju's Answer Standard VIII Mathematics Cube How many mini... Question

How many minimum number of cuts are required if a cube of volume 729 cubic units is to be cut into unit cubes?

A 12 B 24 C 36 D 54 Open in App Solution

The correct option is B 24

Suggest Corrections 0 SIMILAR QUESTIONS

Q.

A wooden cube with edge length ‘n’ (>2) units is painted red all over. By cutting parallel to faces, the cube is cut into

n 3

smaller cubes each of unit edge length. If the number of smaller cubes with just one face painted Red is equal to the number of smaller cubes completely un painted, then n=

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A cube of side 5 cm is cut into as many as 1cm cubes as possible . How many squares will be cut ?

Q. The given cube with integral side length is painted on the outside and is cut into various identical unit cubes. Which of these could be the number of cubes which are not painted?

Q. How many minimum number of cuts are required if a cube of volume 729 cubic units is to be cut into unit cubes?Q. If all the faces of a cube are painted, and 9 cuts are made on it, such that the cube gets divided into maximum number of identical cubes. How many small cubes will not have any painted faces?

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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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[Solved] A cube is painted and cut into 729 smaller and identical cub

The logic follows here is: We know, 93 = 729 Therefore, It will have 9 × 9 cubes in a plane of cubes. So, The number of smaller cubes

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A cube is painted and cut into 729 smaller and identical cubes by making the minimum possible number of cuts. How many smaller cubes have exactly two painted faces?

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24 36 32 84

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Detailed Solution

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The logic follows here is:

We know, 93 = 729 Therefore,

It will have 9 × 9 cubes in a plane of cubes.

So, The number of smaller cubes has exactly two painted faces = (n - 2) × 12

⇒ (9 - 2) × 12 ⇒ 7 × 12 ⇒ 84

Hence, the correct answer is 84.

Additional Information

If a cube has been painted red, blue, and black on pairs of opposite faces and divide it into X parts.

1) Total number of cubes = X3

2) Cubes that have three faces painted = 8 (Because there are only 8 corners in the cube)

3) Cubes which has only two faces painted = (X - 2) × No of Edges (12)

4) Cubes that have only one face painted = (X - 2)2 × 6

5) Cubes that have no face painted = (X - 2)3

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More Cube and Dice Questions

Q1. How many squares are there in the given figure?Q2. A dice is numbered from 1 to 6. Which number is opposite to 1?Q3. A cube is made by folding the given sheet. In the cube so formed, which symbol will be on the face opposite to the face having the symbol '$'?Q4. A cube painted entirely red is cut into 27 small cubes of the same size. How many small cubes have only one surface painted?Q5. What is the probability of getting an even number when a die is thrown?Q6. A cube whose each corner is named as A, B, C, D, F, G and H is segmented into 27 equal tiny cubes. Before dividing the cube, each face of its varnished with different colours. How many tiny cubes will be formed having more than one colour?Q7. In a standard cube, 1 and 3 are written on the visible faces. What will be the sum of the digits on the opposite faces?Q8. In a standard cube, 1 and 3 are written on the visible faces. What will be the sum of the digits on the opposite faces?Q9. Four different positions of the same dice are shown. Select the number that will be on the face opposite to the one having '1'.Q10. Select the box that CANNOT be formed by folding the given sheet along the lines.

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Q1. The sequence of folding a piece of paper and the manner in which the folded paper has been cut is shown in the following figures. How would this paper look when unfolded?Q2. Select the correct mirror image of the given figure when the mirror is placed at the right side.Q3. Select the option in which the given figure is embedded (rotation is NOT allowed).Q4. Which answer figure will satisfy the question? Question Figure:Q5. How many squares are there in the given figure?Q6. A dice is numbered from 1 to 6. Which number is opposite to 1?Q7. Which one of the following alternatives will perfectly complete the given figure?Q8. If a mirror is placed on the shaded line, then which of the following options is the mirror image of the given figure?Q9. A cube is made by folding the given sheet. In the cube so formed, which symbol will be on the face opposite to the face having the symbol '$'?Q10. The time in the clock is 12 ∶ 35. Then its mirror image will be:

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