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A thin piece of wire 40 meters long is cut into two pieces. One piece

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A thin piece of wire 40 meters long is cut into two pieces. One piece [#permalink]

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New post 14 Jun 2009, 23:35
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64% (01:23) correct 36% (01:32) wrong based on 127 sessions

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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 square regions in terms of R.

1) \(\pi R^2\)
2) \(\pi R^2 + 10\)
3) \(\pi R^2 + 1/4\pi^2R^2\)
4) \(\pi R^2 + (40 - 2\pi R)^2\)
5) \(\pi R^2 + (10 - 1/2\pi R)^2\)

[Reveal] Spoiler:
4) or 5) is a given, I just dont see how you make the calculation necessary.


OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-thin-piece ... 06671.html
[Reveal] Spoiler: OA

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Re: A thin piece of wire 40 meters long is cut into two pieces. One piece [#permalink]

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New post 15 Jun 2009, 00:15
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Answer is E

Given:
40 meters long wire cut into two pieces.

Now Length of piece one = circumference of a circle with radius R = \(2\pi R\)

Length of piece two = perimeter of a square created using the remaining wire = \(40-2\pi R\)

\(\Rightarrow \text{length of each side of square} = \frac{40-2\pi R}{4}\)

\(= \frac{4(10-\frac{1}{2}\pi R)}{4}\)

\(= 10-\frac{1}{2}\pi R\)

Now
\(\text{Area of circle} = \pi R^2\)
\(\text {Area of square} = (10-\frac{1}{2}\pi R)^2\)

\(\text {Sum of the areas}=\pi R^2 + (10-\frac{1}{2}\pi R)^2\)

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Re: A thin piece of wire 40 meters long is cut into two pieces. One piece [#permalink]

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New post 15 Jun 2009, 02:01
Option 'E' is correct.
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Re: A thin piece of wire 40 meters long is cut into two pieces. One piece [#permalink]

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New post 07 Jan 2012, 10:49
GREAT EXPLANATION NOOKWAY. THANK YOU
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Re: A thin piece of wire 40 meters long is cut into two pieces. One piece [#permalink]

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New post 10 May 2016, 11:10
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Re: A thin piece of wire 40 meters long is cut into two pieces. One piece [#permalink]

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New post 21 Dec 2017, 23:09
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. \(\pi*r^2 + (10 - \frac{1}{2}\pi*r)^2\)

The area of a circle will be - \(\pi{r^2}\) and \(2\pi{r}\) meters of wire will be used;
There will be \(40-2\pi{r}\) meters of wire left for a square. Side of this square will be \(\frac{40-2\pi{r}}{4}=10-\frac{\pi{r}}{2}\), hence the area of the square will be \((10-\frac{\pi{r}}{2})^2\).

The total area will be - \(\pi{r^2}+(10-\frac{\pi{r}}{2})^2\).

Answer: E.

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Re: A thin piece of wire 40 meters long is cut into two pieces. One piece   [#permalink] 21 Dec 2017, 23:09
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