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Answer: D. 2r^2</h3>
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Explanation:
The radius of the circle is r, which doubles to 2r to get the diameter. The diameter of the circle is also the diagonal of the square. Consequently, this means we have two right triangles in which they have the same hypotenuse of 2r.
Let x be the side length of the square. Use the pythagorean theorem to isolate x
a^2 + b^2 = c^2
x^2 + x^2 = (2r)^2
2x^2 = 4r^2
x^2 = 2r^2 ... divide both sides by 2
x = sqrt(2r^2) ... apply the square root to both sides; keep in mind that x > 0
x = sqrt(r^2*2)
x = sqrt(r^2)*sqrt(2)
x = r*sqrt(2)
The side length of the square is r*sqrt(2)
Therefore, the area of the square is
Area = (side)*(side)
Area = ( r*sqrt(2) )*( r*sqrt(2) )
Area = r*r * sqrt(2)*sqrt(2)
Area = r^2 * sqrt(2*2)
Area = r^2 * sqrt(4)
Area = r^2 * 2
Area = 2r^2
