Geometry and TrigonometryMediumArc length of a quarter circle
Geometry and Trigonometry practice question
A circle has a radius of 5 inches. What is the length, in inches, of an arc that measures 90°? (Give your answer as a multiple of π, written without the π symbol.)
Answer: 2.5 or 5/2
The circumference is 10π, and 90° is a quarter of the circle: 10π/4 = 2.5π. The multiple is 2.5.
Common wrong answers
- If you answered 5
- 5 is half the circumference's multiple (a 180° arc) — or the radius.
- If you answered 10
- 10 is the full circumference's multiple.
- If you answered 6.25
- 6.25 is the quarter-circle's AREA multiple (25π/4), not the arc length.
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