SAT Area and volume Practice Question 14 (Medium)

Math · Geometry and TrigonometryMedium

A circle with a radius of $4$ inches is inscribed in a square, so that the circle touches all four sides of the square. What is the area, in square inches, of the region inside the square but outside the circle?

$16 - 4\pi$

$64 - 8\pi$

$32 - 16\pi$

$64 - 16\pi$

Show answer and explanation

Answer: D

The circle's diameter, $8$ inches, equals the side length of the square, so the square's area is $8^2 = 64$ . The circle's area is $\pi(4)^2 = 16\pi$ . The region between them has area $64 - 16\pi$ square inches.

Choice A uses $4$ as the side length of the square, but the side equals the diameter, $8$ .

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