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# how is the area of the circle calculated?

### 3 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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Have to cut Squares of 14cm * 14cm = 196, then inscribe in them circles of diameter = 14cm

Then Numbers of discs will be  14, 700 / 196 = 75 discs

each square of 196 Cm2  , will have  196- 49π = 42.06 as waste.

Total waste = 42.06 * 75 = 3154.5 cm2

Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
5.0 5.0 (3 lesson ratings) (3)
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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 (honeycomb-like) pattern, starting with 5 disks along the 70-cm 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 14,700-11,853=2847 cm² will be left over.
Brad M. | Professional Tutor: STEM plus Business, Acc'ting, Investment, EditingProfessional Tutor: STEM plus Business,...
4.9 4.9 (222 lesson ratings) (222)
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Hey Ganga -- one method is to line up 5 rows and 15 columns of 14cm discs ...

the 75 discs will leave about 20-25% scrap depending on sawdust produced ...

thin blade / no sawdust ==> 75 discs leaves about 300 sq.cm scrap.

thick blade w/ sawdust may require 5,4,5,4 ... 5 alternating "staggered" columns

=> 68 discs, with about 1000 sq.cm more scrap ~ 1300 sq.cm ... Best regards :)