Question 951521: what is the maximum number of circular plates of radius 2 cm each that can be cut out from a rectangular plate of 20cm *24cm size
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i would take a guess at 30.
each circular plate is inscribed in a square that is 4 by 4.
24/4 = 6 squares going across horizontally.
20/4 = 5 squares going across vertically.
5*6 = 30
i thought of staggering the rows so that the circles can mesh with each other better but that arrangement won't work so it was discarded.
it won't work because you would have to alternate a row of 6 with a row of 5.
in order to get more circles, you would need 3 rows of 6 and 3 rows of 5.
you can't, however, get that, so stacking them side by side and on top of each other appears to be the only solution that will maximize the number of circles in the rectangle.
with the meshed arrangement, the height of 2 rows is less than the height of 2 rows when they are stacked on top of each other, but it's not enough to allow for an extra row that would be required to make the total number of circles greater.
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