SAT Area and volume Practice Question 7 (Hard)

Math · Geometry and TrigonometryHard

A square is inscribed in a circle, so that all four vertices of the square lie on the circle. If the area of the circle is $50\pi$ square units, what is the area, in square units, of the square?

$100$

$50$

$200$

$25\pi$

Show answer and explanation

Answer: A

From $\pi r^2 = 50\pi$ , $r^2 = 50$ . The diagonal of the inscribed square is a diameter of the circle, so the diagonal is $2r$ . A square's area is half the square of its diagonal: $\frac{(2r)^2}{2} = 2r^2 = 2(50) = 100$ .

Choice B uses $r^2$ as the square's area, which would require the side of the square to equal the radius.

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