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

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Director
Joined: 06 Feb 2006
Posts: 897
A thin piece of wire 40 meters long is cut into two pieces. [#permalink]

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28 Oct 2006, 03:25
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45% (medium)

Question Stats:

66% (02:43) correct 34% (01:24) wrong based on 167 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 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. $$\pi*r^2 + (10 - \frac{1}{2}\pi*r)^2$$

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-thin-piece-of-paper-40-mt-long-106671.html
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39701
Re: A thin piece of wire 40 meters long is cut into two pieces. [#permalink]

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28 Nov 2012, 03:20
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nelz007 wrote:
Is there any other way to solve this question?

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 - $$\pi{r^2}+(10-\frac{\pi{r}}{2})^2$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-thin-piece-of-paper-40-mt-long-106671.html
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Joined: 30 Aug 2006
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28 Oct 2006, 03:54
E

((40 - 2pir)/4)^2 + pir^2

(10 - 1/2pir) ^2 + pir^2
Manager
Joined: 21 Sep 2012
Posts: 236
Re: A thin piece of wire 40 meters long is cut into two pieces. [#permalink]

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28 Nov 2012, 01:41
Is there any other way to solve this question?
Re: A thin piece of wire 40 meters long is cut into two pieces.   [#permalink] 28 Nov 2012, 01:41
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