Wire Cut into 2 Pieces

Expert replies

rapper: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed Oct 17, 2012 11:48 am; Location: Mysore

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 ?

Source: Beat The GMAT — Quantitative Reasoning | Mon Oct 22, 2012 4:16 pm

\'manpreet singh: Master | Next Rank: 500 Posts; Posts: 271; Joined: Tue May 22, 2012 3:22 amFollowed by: 3 members; Thanked: 7 times

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!

=======================================
Singh

If you like the post take time to click "thanks" button

There is only one success--to be able to spend your life in your own way.

Last edited by \'manpreet singh on Wed Oct 24, 2012 8:50 pm, edited 2 times in total.

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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 2πr

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

In other words, the perimeter of the square will be 40 - 2πr

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

Brent Hanneson - Creator of GMATPrepNow.com

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

\'manpreet singh: Master | Next Rank: 500 Posts; Posts: 271; Joined: Tue May 22, 2012 3:22 amFollowed by: 3 members; Thanked: 7 times

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

Featured schoolRound 2 closes Jan 7, 2027 54 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review