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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
A thin piece of wire 40 meters long is cut into two pieces. One piece
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30 Mar 2022, 04:50
30 Mar 2022, 04:50
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A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with 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?
A. \(\pi*r^2\)
B. \(\pi*r^2 + 10\)
C. \(\pi*r^2 + \frac{1}{4}*\pi^2*r^2\)
D. \(\pi*r^2 + (40 - 2\pi*r)^2\)
E. \(\pi*r^2 + (10 - \frac{1}{2}\pi*r)^2\)
A. \(\pi*r^2\)
B. \(\pi*r^2 + 10\)
C. \(\pi*r^2 + \frac{1}{4}*\pi^2*r^2\)
D. \(\pi*r^2 + (40 - 2\pi*r)^2\)
E. \(\pi*r^2 + (10 - \frac{1}{2}\pi*r)^2\)
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Joined: 10 Apr 2015
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Re: A thin piece of wire 40 meters long is cut into two pieces. One piece
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30 Mar 2022, 05:21
30 Mar 2022, 05:21
1
GeminiHeat wrote:
A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with 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?
A. \(\pi*r^2\)
B. \(\pi*r^2 + 10\)
C. \(\pi*r^2 + \frac{1}{4}*\pi^2*r^2\)
D. \(\pi*r^2 + (40 - 2\pi*r)^2\)
E. \(\pi*r^2 + (10 - \frac{1}{2}\pi*r)^2\)
A. \(\pi*r^2\)
B. \(\pi*r^2 + 10\)
C. \(\pi*r^2 + \frac{1}{4}*\pi^2*r^2\)
D. \(\pi*r^2 + (40 - 2\pi*r)^2\)
E. \(\pi*r^2 + (10 - \frac{1}{2}\pi*r)^2\)
approach is to plug in a value for r and see what the output should be.
Let's say r = 0. That is, the radius of the circle = 0
This means, we use the ENTIRE 40-meter length of wire to create the square.
So, the 4 sides of this square will have length 10, which means the area = 100
So, when r = 0, the total area = 100
We'll now plug r = 0 into the 5 answer choices and see which one yields an output of 100
A) π(0²) = 0 NOPE
B) π(0²) + 10 = 10 NOPE
C) π(0²) + 1/4(π² * 0²) = 0 NOPE
D) π(0²) + (40 - 2π0)² = 1600 NOPE
E) π(0²) + (10 - 1/2π(0))² = 100 PERFECT!
Answer: E
Cheers,
Brent
Re: A thin piece of wire 40 meters long is cut into two pieces. One piece
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04 Feb 2025, 08:38
04 Feb 2025, 08:38
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