Geometry and TrigonometryMediumSquare with a quarter circle removed
Geometry and Trigonometry practice question
A quarter circle of radius 6 is cut from one corner of a square with side length 6, using that corner as the centre of the circle. What is the area of the remaining piece of the square?
- A. 36 − 9πCorrect
- B. 36 − 36π
- C. 36 − 3π
- D. 36 − 12π
Answer: A. 36 − 9π
Square area: 36. A full circle of radius 6 has area 36π; a quarter of it is 9π. Remaining: 36 − 9π.
Why the other answers are wrong
- B. 36 − 36π
- 36π is a FULL circle of radius 6, which wouldn't even fit in the square.
- C. 36 − 3π
- 3π uses half the radius... no: (1/4)π(6²) = 9π, not 3π.
- D. 36 − 12π
- 12π is a third of the circle, but a quarter circle is removed.
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