A square has a perimeter of 48 units. If a circle is inscribed within this square, what is the area of the region inside the square but outside the circle?

A 144 - 36π

B 36 - 9π

C 144 - 12π

D 12 - 3π

✓ Correct Answer: Option A

The side length of the square is 48/4 = 12 units. Its area is 12^2 = 144. The diameter of the inscribed circle is equal to the side length, so its radius is 12/2 = 6 units. The area of the circle is π(6^2) = 36π. The shaded area is 144 - 36π.

💡 Why is A) the correct answer?

The correct answer to the question "A square has a perimeter of 48 units. If a circle is inscribed within this square, what is the area of the region inside the square but outside the circle?" is Option A: 144 - 36π.

The other options — B) 36 - 9π, C) 144 - 12π, D) 12 - 3π — are incorrect for this GRE Exam Prep question. As explained above: The side length of the square is 48/4 = 12 units. Its area is 12^2 = 144. The diameter of the inscribed circle is equal to the side length, so its radius is 12/2 = 6 units. The area of the circle is …

📚 About This GRE Exam Prep Practice Question

This 3-level GRE Exam Prep question from the Quantitative Reasoning topic is part of BrainForge Quiz's free exam preparation library. Each question includes the correct answer and a detailed explanation to help you understand the underlying concept, not just memorize the answer.

How to use this page: Read the question above, consider all four options (A through D), then check the highlighted correct answer and explanation. For active timed practice, start a free GRE Exam Prep practice test or use flashcards for spaced repetition review.

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A square has a perimeter of 48 units. If a circle is inscribed within this square, what is the area of the region inside the square but outside the circle?

✓ Correct Answer: Option A

📚 About This GRE Exam Prep Practice Question

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