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. πr²
B. πr² +10
C. πr² + 1/4 π²r²
D. πr² + (40-2πr)²
E. πr² + (10 - (1/2)πr)²
Let r=0, so that the ENTIRE wire is used to form the square.
Perimeter of the square = 40.
Each side of the square = 40/4 = 10.
Area of the square = 10² = 100.
Area of the circle + area of the square = 0 + 100 = 100. This is our target.
Now we plug r=0 into the answers to see which yields our target of 100.
A quick scan reveals that only
E works:
πr² + (10 - 1/2πr)² = 0 + 10² = 100.
The correct answer is
E.
Last edited by
GMATGuruNY on Sat Sep 29, 2012 12:46 pm, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
