Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryMedium
A civil engineer is designing a circular traffic roundabout with a radius of 20 meters. A pedestrian walkway is planned along the circumference. If the engineer needs to determine the length of an arc spanning a central angle of 90 degrees for a specific section of the walkway, what is the length of this arc?
- A10π meters
- B20π meters
- C40π meters
- D5π meters
Show answer & explanationAnswer & explanation
Correct answer: A. 10π meters
The length of an arc is calculated using the formula L = (θ/360°) × 2πr, where θ is the central angle in degrees and r is the radius. Substitute the given values (θ=90°, r=20m) into the formula.
Why the other options are wrong
- B. This is incorrect; it is half the circumference, corresponding to a 180° angle.
- C. This is incorrect; it is the full circumference, corresponding to a 360° angle.
- D. This is incorrect; it might be the result of using a radius of 10 or an incorrect fraction of the circumference.
Arc Length of a Circle
The distance along the curved edge of a sector of a circle, proportional to the central angle.
- Calculated as a fraction of the circle's full circumference.
- Formula: L = (θ/360°) × 2πr (for θ in degrees).
- Formula: L = θr (for θ in radians).
Memory trick: Arc length: a 'Fraction' of the 'Circumference'!