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 + 1/4 pi^2 r^2
D. pi r^2 + (40-2pi r)^2
E. pi r^2 + (10 - 1/2 pi r)^2
Plug in r = 4.
Area of circle = �r² = �4² = 16� ≈ 48
Circumference of circle = 2�r = 8� ≈ 24.
Perimeter of square = remaining wire = 40-24 = 16.
Side of square = 16/4 = 4.
Area of square = 4^2 = 16.
Area of circle + area of square ≈ 48+16 ≈ 64. This is our target.
Now we plug r=4 into all the answers to see which yields our target of 64.
Only answer choice E works:
pi r^2 + (10 - 1/2 pi r)^2 ≈ 3*(4²) + (10 - 1/2*3*4)² = 48+16 = 64.
The correct answer is
E.
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
