Question 205500: Compare the area of the circle with the maximum area of the rectangular (square) shape. How much larger is the area of the circle? Found 2 solutions by Alan3354, Targetweek:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! If the Diameter of each shape is 1
then the area of the circle is pi and the "square" is 1
so the ratio of circle to "square" is pi/1
if D=2
then the ratio is pi/2
if D=3
then the ratio is pi/3
it appears that it is a series where if D=n then the ratio is pi/n
when D=1/4 the circle is .723 larger
when D=1/2 the circle is 1.31 larger
when D=1 then the circle is about 2.142(let's say square inches for fun) larger
when D=2 the circle is about 2.283 larger
when D=3 the circle is about .423 larger
when D=4 the circle is 3.437 smaller
when D=5 the circle is ...
i used microsoft excel to extrapolate or get more values and here is what i came up with
Diameter difference
0.00390625 0.0123
0.0625 0.1924
0.250 0.7229
0.500 1.3208
1.000 2.1416
1.500 2.4624
2.000 2.2832
2.500 1.6040
3.000 0.4248
3.500 -1.2544
4.000 -3.4336
4.500 -6.1128
5.000 -9.2920
5.500 -12.9712
6.000 -17.1504
6.500 -21.8296
7.000 -27.0089
7.500 -32.6881
8.000 -38.8673
8.500 -45.5465
9.000 -52.7257
9.500 -60.4049
10.000 -68.5841
10.500 -77.2633
11.000 -86.4425
11.500 -96.1217
12.000 -106.3009
12.500 -116.9801
13.000 -128.1593
13.500 -139.8385
14.000 -152.0177
14.500 -164.6969
15.000 -177.8761
15.500 -191.5553
16.000 -205.7345
16.500 -220.4137
17.000 -235.5929
17.500 -251.2721
18.000 -267.4513
then i used excel to graph them but i don't think i can paste a graph into this but the line appears to be a parabola the limit as x->0+ is 0 i think the equation to sum up the relationship would be...
i went to another website and used a regression tool and calculate the exponential regresssion (yes i did check the equation by plugging them back in)
and the equation is y = -1 x^2 + 3.1416x + 3.2226e-7
i hope that helps
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