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

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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, 23:35
Bunuel 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. \(\pi*r^2 + (10 - \frac{1}{2}\pi*r)^2\)

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]

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New post 22 Dec 2017, 00:07
shivamtibrewala wrote:
Bunuel 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. \(\pi*r^2 + (10 - \frac{1}{2}\pi*r)^2\)

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]

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New post 22 Dec 2017, 00:07
shivamtibrewala wrote:
Bunuel 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. \(\pi*r^2 + (10 - \frac{1}{2}\pi*r)^2\)

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.



Could you please share some extra questions which are similar to this?


23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations




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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 23 Jun 2018, 02:20
Hi friends,

Today I came across this question in a GMAT prep exam and I really can't figure out what I am doing wrong. I consistently arrive to answer C though I perfectly understand how to get to option E. Here is my reasoning:

Area of the circle: \(π*r^{2}\)

Area of the square:
Since there are 20 meters of wire to make the square, then each side of the square must have 5 meters long.
If \(2*π*r=20\), then \(r=\frac{10}{π}\)
In order to represent the side of the square (5 meters long) in terms of \(r\), I say that \(side of the square=r*\frac{π}{2}=\frac{10}{π}*\frac{π}{2}=5\). So \(area of the square=(r*\frac{π}{2})^2=\frac{1}{4}∗π^2∗r^2\)

Total area: \(πr^{2}+\frac{1}{4}∗π^2∗r^2\)

Option C :idontknow:

It would help me a lot if somebody could tell me where is the flaw in my method.
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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 14 May 2019, 01:56
\(40-2\pi{r}\) meters of wire are left for the square means that \(40-2\pi{r}\) is the perimeter of the square so the side of it will be \(\frac{40-2\pi{r}}{4}=10-\frac{\pi{r}}{2}\).[/quote]

How did you brain function to solve this question in less than 2mins! :) :thumbup:
I got nervous and then struggled to find a solution which was incorrect. :?
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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 25 Aug 2019, 22:23
anilnandyala 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. \(\pi*r^2 + (10 - \frac{1}{2}\pi*r)^2\)


Given: 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.

Asked: Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r?

Let the cut divide the wire into 2 pieces \(2\pi r\ and\ 40 - 2\pi r\)

Total area = \(\pi r^2 + (\frac{40 - 2\pi r}{4})^2 = \pi*r^2 + (10 - \frac{1}{2}\pi*r)^2\)

IMO E
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Re: A thin piece of wire 40 meters long is cut into 2 pieces. 1  [#permalink]

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Re: A thin piece of wire 40 meters long is cut into 2 pieces. 1   [#permalink] 07 Oct 2019, 08:41

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