2012-05-03 09:00:19

The area of a circle is 64π. If a square were drawn inside that circle, what is the largest possible area of that square?

(A) 16 square units
(B) 32 square units
(C) 64 square units
(D) 128 square units
(E) 256 square units

The correct answer is D

Explanation: The largest possible square that can be contained in that circle would be one that has a diagonal that is identical to the circle's diameter. This circle's diameter must be 16, since area is πr², and here πr² = 64π, making r² = 64, and r = 8. Since diameter is 2π, then the diameter here is 16. This is also the diagonal of the square.

In squares, the diagonal is proportional to the side lengths so that, if s = the length of the side, then the diagonal is s√2. Here, then, 16 = x√2, meaning 16/√2 = s. Since the area of a square is found by squaring the length of one side, the area of this square can be found by squaring 16/√2 to get (16/√2)², which is (16ç)/(√2²), or 256/2, which simplifies to 128 square units, making choice D correct.