A piece of construction paper is .01mm thick. It is cut in half and one piece is placed on top of the other to make a pile. These are cut in half, and all four pieces are placed in a pile. These four are cut in half and placed in a pile, and the process is continued. After the pieces have been cut and piled for the tenth time, what is the height of the pile in cm?: *
2.012 cm
1.024 cm
1.648 cm
0.864 cm
Please explain, thanks
I will be happy to critique your thinking.
To find the height of the pile after ten cuts, we need to calculate the total thickness of all the paper pieces combined.
Each time we cut the paper in half, we end up with two equal pieces. Thus, each time we cut, the height of the pile doubles.
Let's start by calculating the height of the pile after the first cut:
Original thickness of the paper = 0.01 mm
After the first cut, we have two pieces, each with a thickness of 0.01 mm. So the combined thickness is: 0.01 mm + 0.01 mm = 0.02 mm.
Now, for the second cut, we double the combined thickness of the previous cut:
Combined thickness after the first cut = 0.02 mm
After the second cut, we have four pieces, each with a thickness of 0.02 mm. So the combined thickness is: 0.02 mm + 0.02 mm = 0.04 mm.
We can continue this process for all ten cuts:
After the third cut: 0.08 mm
After the fourth cut: 0.16 mm
After the fifth cut: 0.32 mm
After the sixth cut: 0.64 mm
After the seventh cut: 1.28 mm
After the eighth cut: 2.56 mm
After the ninth cut: 5.12 mm
After the tenth cut: 10.24 mm
We now convert the final thickness from millimeters to centimeters:
10.24 mm = 1.024 cm
Therefore, the height of the pile after ten cuts is 1.024 cm.
Hence, the correct answer is 1.024 cm.