Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A landscaper is designing a flower bed that is a sector of a circle. The radius of the sector is 6 meters, and the central angle is 60 degrees. What is the approximate area of the flower bed?
- A18.85 m²
- B9.42 m²
- C37.70 m²
- D56.55 m²
Show answer & explanationAnswer & explanation
Correct answer: A. 18.85 m²
The area of a sector of a circle is given by the formula A = (θ/360°) * πr², where θ is the central angle in degrees and r is the radius. Given θ = 60° and r = 6 meters, the area is A = (60/360) * π * (6)² = (1/6) * π * 36 = 6π. Using π ≈ 3.14159, A ≈ 6 * 3.14159 ≈ 18.8495 m², which is approximately 18.85 m².
Why the other options are wrong
- B. This is the arc length of the sector, not the area.
- C. This is the area of a sector with a central angle of 120 degrees, or 2 * 6π.
- D. This is 9π * 2, possibly from confusion with volume or incorrect area calculation.
Area of a Circular Sector
The area of a portion of a circle enclosed by two radii and an arc.
- Formula: A = (θ/360°) * πr² (where θ is in degrees).
- Alternatively: A = (1/2)r²θ (where θ is in radians).
- It's a fraction of the total area of the circle.
Memory trick: Sector is a 'Slice' of the whole pie.