(2) On the basis of previous work, six floors were added up and down, and now there are eight floors in * * *.
(3) Finally, one layer can be added up and down, but each layer can only be one layer, *** 10, so that the number of squares in each layer can be obtained.
Answer: Answer: You can cut 66 small squares. ( 1)
—————————————— I am the dividing line ————————————
Method 1:
(1) We put 10 small squares in a row, and as a long rectangle, it can just fit into a circle with a diameter of 10.05cm, as shown in the figure, rectangular ABCD. ..
∫AB = 10BC = 10。
∴ Diagonal AC2 =100+1=1kloc-0/<10.052. (3 points)
(2) We can put 9 small squares above and below the rectangular ABCD.
∫ The newly added two rows of small squares, plus a part of ABCD, can be regarded as a rectangular EFGH. The length of the rectangle EFGH is 9, the height is 3, and the diagonal eg2 = 92+32 = 81+9 = 90 <10.052. But the newly added two rows of small squares can't be 10 per row, because
102+32 =100+9 =109 >10.052. (6 points)
(3) Similarly: 82+52 = 64+25 = 89 < 10.052,
92+52=8 1+25= 106> 10.052,
Eight small squares can be arranged above and below the rectangular EFGH, so there are now five layers of small squares. (8 points)
(4) On the basis of the original, add another layer up and down, ***7 layers, and the height of the new rectangle can be regarded as 7, so the new two rows can be 7 but not 8.
∵72+72=49+49=98< 10.052,
82+72 = 64+49 =113 >10.052. (9 points)
(5) On the basis of 7 layers, add another layer up and down, and the height of the new rectangle can be regarded as 9. Each row of these two layers can be 4, but not 5.
∵42+92= 16+8 1=97< 10.052,
52+92=25+8 1= 106> 10.052,
At present, there are 9 floors in total, with a height of 9, leaving a space of about 0.5cm above and below, because the position of rectangular ABCD cannot be adjusted.
Therefore, there is no room for Little Square.
∴ 10+2×9+2×8+2×7+2×4=66 (pieces). (10)
Method 2:
Students can also be arranged according to the following methods, as long as the reasoning is clear, and the scoring standard refers to the method 1.
You can arrange 9 squares in a row, stack 4 layers, and put them in the circle first.
Then: (1) add one more layer above and below, with 8 layers, and now there are 6 layers in * * * *;
(2) On the basis of the previous one, there are six upper and lower floors, and now * * * * has eight floors;
(3) Finally, one floor can be added up and down, but each floor can only be one floor, *** 10.
So * * * has: 4×9+2×8+2×6+2× 1=66 (pieces).
After the solution, you can also understand that it is simpler to divide directly by area, and there is no loss.
I hope it can be adopted. I wish you a smooth study in the future.