Question

a. sector area = radius × central angle (in degrees)
b. sector area = 2 × radius × central angle
c. sector area = 0.5 × radius² × central angle (in radians)
d. sector area = circumference × central angle (in degrees)
what is the formula for calculating sector area in a circle?
a. arclength = diameter × central angle (in degrees)
b. arclength = radius × central angle (in radians)
c. arclength = circumference × central angle (in degrees)
d. arclength = 2 × radius × central angle (in radians)
what is the formula for calculating arc length in a circle?

Explanation:

• For the sector area formula:
• The formula for the area of a sector of a circle when the central angle \(\theta\) is in radians is \(A=\frac{1}{2}r^{2}\theta\) (where \(r\) is the radius). This can be rewritten as \(A = 0.5\times Radius^{2}\times CentralAngle\) (in radians).
• For the arc - length formula:
• The formula for the arc - length \(l\) of a circle when the central angle \(\theta\) is in radians is \(l = r\theta\) (where \(r\) is the radius).

Answer:

• For the sector area formula: c. \(SectorArea=0.5\times Radius^{2}\times CentralAngle\) (in radians)
• For the arc - length formula: b. \(ArcLength = Radius\times CentralAngle\) (in radians)