Question

1. what is the formula for calculating sector area in a circle?

a. sector area = 0.5×radius²×central angle (in radians)
b. sector area = circumference×central angle (in degrees)
c. sector area = 2×radius×central angle
d. sector area = radius×central angle (in degrees)

Explanation:

Step1: Recall the formula for the area of a sector

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 of the circle and \(\theta\) is the central angle). This can be rewritten as \(A = 0.5\times Radius^{2}\times Central\ Angle\ (in\ radians)\)

Step2: Analyze other options

• Option b: The formula \(Sector\ Area=Circumference\times Central\ Angle\ (in\ degrees)\) is incorrect. The circumference \(C = 2\pi r\), and there is no such relation for the area of a sector.
• Option c: The formula \(Sector\ Area=2\times Radius\times Central\ Angle\) is incorrect. There is no basis for this formula in the context of circle - sector area calculation.
• Option d: The formula \(Sector\ Area=Radius\times Central\ Angle\ (in\ degrees)\) is incorrect. The standard formula does not have this form.

Answer:

A. Sector Area \(= 0.5\times Radius^{2}\times Central\ Angle\ (in\ radians)\)