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Intern  B
Joined: 02 Nov 2017
Posts: 17
Re: A thin piece of wire 40 meters long is cut into two pieces. One piece  [#permalink]

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

Could you please share some extra questions which are similar to this?
Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Re: A thin piece of wire 40 meters long is cut into two pieces. One piece  [#permalink]

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

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

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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Re: A thin piece of wire 40 meters long is cut into two pieces. One piece  [#permalink]

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

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

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Intern  B
Joined: 05 Apr 2018
Posts: 3
Re: A thin piece of wire 40 meters long is cut into two pieces. One piece  [#permalink]

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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 It would help me a lot if somebody could tell me where is the flaw in my method.
Intern  B
Joined: 16 Mar 2017
Posts: 12
Re: A thin piece of wire 40 meters long is cut into two pieces. One piece  [#permalink]

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$$40-2\pi{r}$$ 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!  I got nervous and then struggled to find a solution which was incorrect. SVP  P
Joined: 03 Jun 2019
Posts: 1723
Location: India
A thin piece of wire 40 meters long is cut into two pieces. One piece  [#permalink]

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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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