The total area of plywood is 210 cm x 70 cm = 14,700 cm².
The area of each disk is pi*(7 cm)²≈ 154 cm², so the theoretical maximum number of disks is 14,700/154 rounded down to the nearest integer, which is 95.
One can show that the actual maximum number of disks is 77. You get them by cutting in a hexagonal (honeycomblike) pattern, starting with 5 disks along the 70cm edge, followed by 4 disks, 5 disks, 4 disks etc. There will be 9 rows where you can cut 5 disks, and 8 rows in between where you can cut 4 disks, for a total of 9x5+8x4=77 disks. You use 77(154 cm²)=11,853 cm² of plywood, so that 14,70011,853=2847 cm² will be left over.
1/5/2014

Andre W.
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