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# A thin piece of wire 40 meters long is cut into 2 pieces. 1

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Manager
Joined: 19 Sep 2005
Posts: 110
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A thin piece of wire 40 meters long is cut into 2 pieces. 1 [#permalink]  08 Nov 2005, 21:19
A thin piece of wire 40 meters long is cut into 2 pieces. 1 piece is used to form a circle w/ radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r?

1. Pi *r^2
2. Pi* r^2 + 10
c. Pi * r^2 + 1/4* Pi^2 * r^2
d. Pi * r^2 + (40 - 2* Pi * r)^2
e. Pi * r^2 + (10 - 1/2 * Pi * r)^2
Manager
Joined: 18 Oct 2005
Posts: 79
Location: Hong Kong
Followers: 1

Kudos [?]: 2 [2] , given: 0

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I choose E.

First component is area of circle. Pi * r^2

Second component should be area of sq.
length left after making circle = 40 - 2*Pi*r
This length will then be used to form a sq with 4 sides. Therefore one side of sq=(40-2*Pi*r)/4
And side * side = area of sq. (10 - 1/2 * Pi * r)^2

1st component + 2nd component = answer
Manager
Joined: 19 Sep 2005
Posts: 110
Followers: 1

Kudos [?]: 3 [0], given: 0

Correct, OA is E.
Wow, you made it look so easy.
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