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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.
What is the minimum number of pieces obtained when 3 cuts are made?
Answer: 4
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.
What is the maximum number of pieces obtained when 3 cuts are made?
Answer: 8
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.
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
6 cuts are made?
Answer: 27
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.
9 cuts are made
Answer: 64
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.
12 cuts are made?
Answer: 125
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 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.
5 cuts are made?
Answer: 18
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 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.
10 cuts are made?
Answer: 80
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 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.
23 cuts are made?
Answer: 648
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 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.
Answer the next 2 questions based on the information given below:
A certain number of cuts are made in a cube.
How many smaller cubes will be obtained when 6 cuts are made?
Answer: 27
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.
How many smaller cubes will be obtained when 5 cuts are made?
Answer: D
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).