Cookie Size Comparison Based on Average Radius
Two Pairs of Cookies
One with average radius of 8 cm
Other with average radius of 7 cm
Which pair of cookies would you prefer?
8-cm Cookie
8-cm Cookie
2 Cookies
…
Total cookie area =
2
p
8
2
= 2
p
(
64)
Area of average
Cookie = 64
p
7-cm Cookie
7-cm Cookie
2 Cookies
…
Total cookie area =
2
p
7
2
= 2
p
(
49)
Area of average
Cookie = 49
p
We are now going to start making two unequal size cookies,
one smaller and one larger, always keeping the average radius
of the two cookies equal to 7 cm, the initial radii of the two cookies.
Each time we will compute the total area of the two cookies and the
average area per cookie..
6-cm Cookie
8-cm Cookie
6-cm Cookie
8-cm Cookie
Total cookie area =
p
8
2
+
p
6
2
= 100
p
= 2
p
(
50)
Area of average
cookie =
(
50)
p
TARGET: Making Area of
average cookie > 64
p
5-cm Cookie
9-cm Cookie
5-cm Cookie
9-cm Cookie
Total cookie area =
p
9
2
+
p
5
2
= 106
p
= 2
p
(
53)
Area of average
cookie =
(
53)
p
TARGET: > 64
p
4-cm
Cookie
10-cm Cookie
4-cm
Cookie
10-cm Cookie
Total cookie area =
p
10
2
+
p
4
2
= 116
p
= 2
p
(
58)
Area of average
cookie =
(
58)
p
TARGET: > 64
p
3-cm
Cookie
11-cm Cookie
3-cm
Cookie
11-cm Cookie
Total cookie area =
p
11
2
+
p
3
2
= 130
p
= 2
p
(
65)
Area of average
cookie =
(
65)
p
TARGET: > 64
p
2-cm
Cookie
12-cm Cookie
2-cm
Cookie
12-cm Cookie
Total cookie area =
p
12
2
+
p
2
2
= 148
p
=2
p
(
74)
Area of average
cookie =
(
74)
p
TARGET: > 64
p
1-
cm
13-cm Cookie
1-
cm
13-cm Cookie
Total cookie area =
p
13
2
+
p
1
2
= 170
p
=2
p
(
85)
Area of average
cookie =
(
85)
p
TARGET: > 64
p
Comparing two pairs of cookies with average radii of 8 cm and 7 cm respectively. Through a series of adjustments to maintain an average radius of 7 cm, the total area, individual areas, and target average area per cookie are calculated for various cookie size combinations. The analysis aims to find the optimal cookie size combination based on area considerations.
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Presentation Transcript
Two Pairs of Cookies One with average radius of 8 cm Other with average radius of 7 cm Which pair of cookies would you prefer?
2 Cookies Total cookie area = 2 82 = 2 (64) Area of average Cookie = 64 8-cm Cookie
2 Cookies Total cookie area = 2 72 = 2 (49) Area of average Cookie = 49 7-cm Cookie We are now going to start making two unequal size cookies, one smaller and one larger, always keeping the average radius of the two cookies equal to 7 cm, the initial radii of the two cookies. Each time we will compute the total area of the two cookies and the average area per cookie..
8-cm Cookie 6-cm Cookie
Total cookie area = 82 + 62 = 100 = 2 (50) TARGET: Making Area of average cookie > 64 Area of average cookie = (50) 8-cm Cookie 6-cm Cookie
9-cm Cookie 5-cm Cookie
Total cookie area = 92 + 52 = 106 = 2 (53) TARGET: > 64 Area of average cookie = (53) 9-cm Cookie 5-cm Cookie
10-cm Cookie 4-cm Cookie
Total cookie area = 102 + 42 = 116 = 2 (58) TARGET: > 64 Area of average cookie = (58) 10-cm Cookie 4-cm Cookie
11-cm Cookie 3-cm Cookie
Total cookie area = 112 + 32 = 130 = 2 (65) TARGET: > 64 Area of average cookie = (65) 11-cm Cookie 3-cm Cookie
12-cm Cookie 2-cm Cookie
Total cookie area = 122 + 22 = 148 =2 (74) TARGET: > 64 Area of average cookie = (74) 12-cm Cookie 2-cm Cookie
13-cm Cookie 1- cm
Total cookie area = 132 + 12 = 170 =2 (85) TARGET: > 64 Area of average cookie = (85) 13-cm Cookie 1- cm
