arfabe16 wrote:Here are two GMAT math problems that I don't know how to solve. I would greatly appreciate your help in figuring out the process
1. 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) πr^2
b) πr^2 + 10
c) πr^2 + (1/4)(π^2)(r^2)
d) πr^2 + (40 - 2πr)^2
e) πr^2 + (10 - .5πr)^2
We can plug in values and ballpark.
Let r = 2, let pi = 3.
Area of circle = 4pi = 12
Circumference = 4pi = 12
Remaining wire = 40-12 = 28. This is the perimeter of the square, so s = 28/4 = 7.
Area of square = 7^2 = 49.
Combined areas = 12+49 = 61. This is our target answer.
Only answer choice E works:
Ï€r^2 + (10 - .5Ï€r)^2 = 3*(2^2) + (10 - .5*3*2)^2 = 12+49 = 61.
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