Geometry and TrigonometryVery hardCircumference from a quarter-sector's area
Geometry and Trigonometry practice question
A sector of a circle has a central angle of 90° and an area of 9π. The circumference of the whole circle can be written as kπ. What is the value of k?
Answer: 12
A 90° sector is a quarter of the circle, so the circle's area is 36π and its radius is 6; the circumference is 12π.
Common wrong answers
- If you answered 6
- 6 is the radius.
- If you answered 18
- 18 is half of 36.
- If you answered 36
- 36 is the area's coefficient, not the circumference's.
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