Geometry and TrigonometryMediumArea between a square and its inscribed circle
Geometry and Trigonometry practice question
A circle is inscribed in a square with side length 10, touching all four sides. What is the area of the region inside the square but outside the circle?
- A. 100 − 25πCorrect
- B. 100 − 10π
- C. 100 − 100π
- D. 100 − 5π
Answer: A. 100 − 25π
The circle touches all four sides, so its diameter is 10 and its radius is 5. Square area 100, circle area π(5²) = 25π. Region: 100 − 25π.
Why the other answers are wrong
- B. 100 − 10π
- 10π is the circle's CIRCUMFERENCE (2π × 5), not its area.
- C. 100 − 100π
- 100π uses the diameter, 10, as the radius. The radius is 5, and 5² = 25.
- D. 100 − 5π
- 5π uses the radius without squaring it. Area is πr² = 25π.
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