# CRE 1 - Maximum / Minimum cubes | LR - Cubes

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**Answer the next 2 questions based on the information given below:**

A certain number of cuts are made in a cube.

**CRE 1 - Maximum / Minimum cubes | LR - Cubes**

What is the minimum number of pieces obtained when 3 cuts are made?

Answer: 4

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**Explanation** :

When a cube is cut by certain number of cuts, minimum pieces are obtained when cut all made along the same axis.

Here we have total 3 cuts hence, to obtain minimum pieces we will make all 3 cuts along the same axis.

∴ We will get 4 pieces along this axis.

Hence, 4.

Workspace:

**CRE 1 - Maximum / Minimum cubes | LR - Cubes**

What is the maximum number of pieces obtained when 3 cuts are made?

Answer: 8

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**Explanation** :

When a cube is cut by certain number of cuts, maximum pieces are obtained when cut all made equally along the 3 axes.

Here we have total 3 cuts hence, to obtain maximum pieces we will make 1 cut along each of the axis.

∴ We will get 2 pieces along each of the axis.

⇒ Total pieces obtained = 2 × 2 × 2 = 8.

Hence, 8.

Workspace:

**Answer the next 6 questions based on the information given below:**

A certain number of cuts are made in a cube. What is the maximum number of pieces obtained when

**CRE 1 - Maximum / Minimum cubes | LR - Cubes**

6 cuts are made?

Answer: 27

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**Explanation** :

When a cube is cut by certain number of cuts, maximum pieces are obtained when cut all made equally along the 3 axes.

Here we have total 6 cuts hence, to obtain maximum pieces we will make 2 cuts along each of the axis.

∴ We will get 3 pieces along each of the axis.

⇒ Total pieces obtained = 3 × 3 × 3 = 27.

Hence, 27.

Workspace:

**CRE 1 - Maximum / Minimum cubes | LR - Cubes**

9 cuts are made

Answer: 64

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**Explanation** :

When a cube is cut by certain number of cuts, maximum pieces are obtained when cut all made equally along the 3 axes.

Here we have total 9 cuts hence, to obtain maximum pieces we will make 3 cuts along each of the axis.

∴ We will get 4 pieces along each of the axis.

⇒ Total pieces obtained = 4 × 4 × 4 = 64.

Hence, 64.

Workspace:

**CRE 1 - Maximum / Minimum cubes | LR - Cubes**

12 cuts are made?

Answer: 125

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**Explanation** :

Here we have total 12 cuts hence, to obtain maximum pieces we will make 4 cuts along each of the axis.

∴ We will get 5 pieces along each of the axis.

⇒ Total pieces obtained = 5 × 5 × 5 = 125.

Hence, 125.

Workspace:

**CRE 1 - Maximum / Minimum cubes | LR - Cubes**

5 cuts are made?

Answer: 18

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**Explanation** :

Here we have total 5 cuts hence, to obtain maximum pieces we will make 2 cuts along 2 axes and 1 cut along the 3rd the axis.

∴ We will get 3 pieces along two axes and 2 pieces along the 3rd axis.

⇒ Total pieces obtained = 3 × 3 × 2 = 18.

Hence, 18.

Workspace:

**CRE 1 - Maximum / Minimum cubes | LR - Cubes**

10 cuts are made?

Answer: 80

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**Explanation** :

Here we have total 10 cuts hence, to obtain maximum pieces we will make 3 cuts along 2 axes and 4 cut along the 3rd the axis.

∴ We will get 4 pieces along two axes and 5 pieces along the 3rd axis.

⇒ Total pieces obtained = 4 × 4 × 5 = 80.

Hence, 80.

Workspace:

**CRE 1 - Maximum / Minimum cubes | LR - Cubes**

23 cuts are made?

Answer: 648

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**Explanation** :

Here we have total 23 cuts hence, to obtain maximum pieces we will make 8 cuts along 2 axes and 7 cut along the 3rd the axis.

∴ We will get 9 pieces along two axes and 8 pieces along the 3rd axis.

⇒ Total pieces obtained = 9 × 9 × 8 = 648.

Hence, 648.

Workspace:

**Answer the next 2 questions based on the information given below:**

A certain number of cuts are made in a cube.

**CRE 1 - Maximum / Minimum cubes | LR - Cubes**

How many smaller cubes will be obtained when 6 cuts are made?

Answer: 27

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**Explanation** :

When a cube is cut by certain number of cuts, the smaller pieces will also be cube only when equal number of cuts are made along the 3 axes.

Here we have total 6 cuts hence, to obtain smaller cubes we will make 2 cuts along each axis.

∴ We will get 3 cubes along each axis.

⇒ Total smaller cubes obtained = 3 × 3 × 3 = 27.

Hence, 27.

Workspace:

**CRE 1 - Maximum / Minimum cubes | LR - Cubes**

How many smaller cubes will be obtained when 5 cuts are made?

- (a)
15

- (b)
18

- (c)
10

- (d)
Not possible

Answer: Option D

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**Explanation** :

When a cube is cut by certain number of cuts, the smaller pieces will also be cube only when equal number of cuts are made along the 3 axes.

Here we have total 5 cuts. 5 cuts cannot be made equally along the 3 axes.

∴ With 5 cuts we cannot get smaller cubes.

Hence, option (d).

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