Let's start with the circle. The length of wire that was used to form the circle isn't important right now, but we're given that this piece of wire formed a circle with radius, r. Therefore, the area of the circle = Pi*(r^2).
Before we find the area of the square, recall that the circumference of a circle with radius, r = 2*Pi*r.
This circumference is, in fact, equal to the length of the wire that was used for forming the circle.
The length of wire that remains to form the square = 40 - 2*Pi*r.
Since a square has 4 equal sides, each side of the square = 1/4 * (40 - 2*Pi*r) = 10 - (Pi*r/2)
The area of a square is the product of two sides which, in this case, equals [(10 - (Pi*r/2)]^2
Looks like the answer is (E)
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Lenght problem
Source: Beat The GMAT — Problem Solving |
equate perimeters of the square and the circle to 40 -> 2Pi*r+4a=40, where a is the side of square. Pi*r+2a=20; a in terms of r will be 2a=20-Pi*r and a=10-Pi*r/2
total squares of circle and square will be Pi*r^2+(10-Pi*r/2)^2
answer e
total squares of circle and square will be Pi*r^2+(10-Pi*r/2)^2
answer e
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