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Wire Cut into 2 Pieces

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Wire Cut into 2 Pieces

by rapper » Mon Oct 22, 2012 4:16 pm
Q1:

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)r2

B. (pi)r2 + 10

C. (pi)r2 + ¼ (pi)^2r^2

D. (pi)r2 + (40-2pr)^2

E. (pi)r2 + (10- ½ (pi)r)^2

Hi i Solved it and got answer D.I dont have its answer,so can anyone help
and let me know is it correct ?
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by \'manpreet singh » Mon Oct 22, 2012 7:44 pm
rapper wrote:Q1:

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)r2

B. (pi)r2 + 10

C. (pi)r2 + ¼ (pi)^2r^2

D. (pi)r2 + (40-2pr)^2

E. (pi)r2 + (10- ½ (pi)r)^2

Hi i Solved it and got answer D.I dont have its answer,so can anyone help
and let me know is it correct ?
Yes the answer is E

Since circle is radius r, therefore the length of the wire forming circle is 2(pi)r

rest of the length 40- 2(pi)r is length of wire forming the square.

Area of circle is (pi)r2

Area of square is 1/2(40-pr)^2=(10- ½ (pi)r)^2

Total area= (pi)r2 + (10- ½ (pi)r)^2 voila!

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Singh

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Last edited by \'manpreet singh on Wed Oct 24, 2012 8:50 pm, edited 2 times in total.
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by Brent@GMATPrepNow » Tue Oct 23, 2012 6:11 am
rapper wrote:Q1:

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 + ¼ (pi)^2r^2

D. (pi)r^2 + (40-2pr)^2

E. (pi)r^2 + (10- ½ (pi)r)^2

Hi i Solved it and got answer D.I dont have its answer,so can anyone help
and let me know is it correct ?

The correct answer is actually E

Since r is the radius of the circle, the area of the circle will be πr^2.
If r is the radius of the circle, the length of wire used for this circle will equal its circumference which is 2Ï€r

So, the length of wire to be used for the square must equal 40 - 2Ï€r

In other words, the perimeter of the square will be 40 - 2Ï€r

Since squares have 4 equal sides, the length of each side of the square will be (40 - 2πr )/4, which simplifies to be 10 - πr/2

If each side of the square has length 10 - πr/2, the area of the square will be (10 - πr/2)^2

So, the total area will equal πr^2 + (10 - πr/2)^2, which is the same as E

Cheers,
Brent
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by Brent@GMATPrepNow » Tue Oct 23, 2012 6:22 am
'manpreet singh wrote:
rapper wrote:Q1:

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)r2

B. (pi)r2 + 10

C. (pi)r2 + ¼ (pi)^2r^2

D. (pi)r2 + (40-2pr)^2

E. (pi)r2 + (10- ½ (pi)r)^2

Hi i Solved it and got answer D.I dont have its answer,so can anyone help
and let me know is it correct ?
Yes the answer is D

Since circle is radius r, therefore the length of the wire forming circle is 2(pi)r

rest of the length 40- 2(pi)r is length of wire forming the square.

Area of circle is (pi)r2

Area of square is (40-2pr)^2

Total area= pi)r2 + (40-2pr)^2 voila!
There's a small problem with the part in blue (above)
40- 2(pi)r represents the entire perimeter of the square.
Before we can find the area, we must find the length of each side. To do so, we need to divide 40- 2(pi)r by 4

Cheers,
Brent
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by \'manpreet singh » Wed Oct 24, 2012 8:46 pm
Brent@GMATPrepNow wrote:
'manpreet singh wrote:
rapper wrote:Q1:

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)r2

B. (pi)r2 + 10

C. (pi)r2 + ¼ (pi)^2r^2

D. (pi)r2 + (40-2pr)^2

E. (pi)r2 + (10- ½ (pi)r)^2

Hi i Solved it and got answer D.I dont have its answer,so can anyone help
and let me know is it correct ?
Yes the answer is D

Since circle is radius r, therefore the length of the wire forming circle is 2(pi)r

rest of the length 40- 2(pi)r is length of wire forming the square.

Area of circle is (pi)r2

Area of square is (40-2pr)^2

Total area= pi)r2 + (40-2pr)^2 voila!
There's a small problem with the part in blue (above)
40- 2(pi)r represents the entire perimeter of the square.
Before we can find the area, we must find the length of each side. To do so, we need to divide 40- 2(pi)r by 4



Yes Brent you are right , thanks for the correction! :) I have edited the answer now
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