Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryMedium
A landscape architect is designing a garden bed in the shape of a sector of a circle. The circular garden has a radius of 10 feet, and the central angle of the sector is 144 degrees. What is the area of this garden bed?
- A20π square feet
- B16π square feet
- C40π square feet
- D80π square feet
Show answer & explanationAnswer & explanation
Correct answer: C. 40π square feet
The area of a circular sector is found by taking a fraction of the total area of the circle, based on the central angle. The formula is A_sector = (θ/360°) × πr², where θ is the central angle in degrees and r is the radius.
Why the other options are wrong
- A. This is incorrect; it might be related to arc length or an incorrect radius.
- B. This is incorrect; it might be the result of an incorrect fraction or calculation.
- D. This is incorrect; it might be the result of a miscalculation of the fraction or radius squared.
Area of a Circular Sector
The area of a portion of a circle enclosed by two radii and an arc, proportional to the central angle.
- Calculated as a fraction of the total circle's area.
- Formula: A_sector = (θ/360°) × πr² (for θ in degrees).
- Can also be calculated as (1/2)r²θ (for θ in radians).
Memory trick: Sector area: a 'Slice' of the 'Total Pie'!