Question

Problem: Steve likes to entertain friends
at parties with “wire tricks.” Suppose he takes a piece of wire 60 inches long and cuts it into
two pieces. Steve takes the first piece of wire
and bends it into the shape of a perfect circle.
He then proceeds to bend the second piece of
wire into the shape of a perfect square. Where
should Steve cut the wire so that the total area
of the circle and square combined is as small
as possible? What is this minimal area? What
should Steve do if he wants the combined area
to be as large as possible?

NEED HELP!!

Answer 1

Area of a circle = pi*r^2
Circumference of a circle = 2(pi)(r)
Area of a square = length of side^2
Circumference of a square = length of side*4

Circle
C in Inches Radius Area
1 0.16 0.08
2 0.32 0.32
3 0.48 0.72
4 0.64 1.27
5 0.80 1.99
6 0.95 2.86
7 1.11 3.90
8 1.27 5.09
9 1.43 6.45
10 1.59 7.96
11 1.75 9.63
12 1.91 11.46
13 2.07 13.45
14 2.23 15.60
15 2.39 17.90
16 2.55 20.37
17 2.71 23.00
18 2.86 25.78
19 3.02 28.73
20 3.18 31.83
21 3.34 35.09
22 3.50 38.52
23 3.66 42.10
24 3.82 45.84
25 3.98 49.74
26 4.14 53.79
27 4.30 58.01
28 4.46 62.39
29 4.62 66.92
30 4.77 71.62
31 4.93 76.47
32 5.09 81.49
33 5.25 86.66
34 5.41 91.99
35 5.57 97.48
36 5.73 103.13
37 5.89 108.94
38 6.05 114.91
39 6.21 121.04
40 6.37 127.32
41 6.53 133.77
42 6.68 140.37
43 6.84 147.14
44 7.00 154.06
45 7.16 161.14
46 7.32 168.39
47 7.48 175.79
48 7.64 183.35
49 7.80 191.07
50 7.96 198.94
51 8.12 206.98
52 8.28 215.18
53 8.44 223.53
54 8.59 232.05
55 8.75 240.72
56 8.91 249.55
57 9.07 258.55
58 9.23 267.70
59 9.39 277.01
60 9.55 286.48

Square
C in Inches Side Length Area
1 0.25 0.06
2 0.50 0.25
3 0.75 0.56
4 1.00 1.00
5 1.25 1.56
6 1.50 2.25
7 1.75 3.06
8 2.00 4.00
9 2.25 5.06
10 2.50 6.25
11 2.75 7.56
12 3.00 9.00
13 3.25 10.56
14 3.50 12.25
15 3.75 14.06
16 4.00 16.00
17 4.25 18.06
18 4.50 20.25
19 4.75 22.56
20 5.00 25.00
21 5.25 27.56
22 5.50 30.25
23 5.75 33.06
24 6.00 36.00
25 6.25 39.06
26 6.50 42.25
27 6.75 45.56
28 7.00 49.00
29 7.25 52.56
30 7.50 56.25
31 7.75 60.06
32 8.00 64.00
33 8.25 68.06
34 8.50 72.25
35 8.75 76.56
36 9.00 81.00
37 9.25 85.56
38 9.50 90.25
39 9.75 95.06
40 10.00 100.00
41 10.25 105.06
42 10.50 110.25
43 10.75 115.56
44 11.00 121.00
45 11.25 126.56
46 11.50 132.25
47 11.75 138.06
48 12.00 144.00
49 12.25 150.06
50 12.50 156.25
51 12.75 162.56
52 13.00 169.00
53 13.25 175.56
54 13.50 182.25
55 13.75 189.06
56 14.00 196.00
57 14.25 203.06
58 14.50 210.25
59 14.75 217.56
60 15.00 225.00

Answer 2

Maximum Combined Area = 59 Inches of wire for Circle = 277.07 inches of Area
Minimum Combined Area = 26 Inches of wire for Circle = 126.04 inches of Area