Question

which of the following is a valid method for calculating the sector area?
a. sector area = π × radius²
b. sector area = 0.5 × radius² × central angle (in radians)
c. sector area = radius × central angle (in radians)
d. sector area = 2 × π × radius
which unit is appropriate for measuring the area of a sector in a circle?
a. degrees
b. square centimeters
c. centimeters
d. meters

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 is in radians is \(A=\frac{1}{2}r^{2}\theta\) (where \(r\) is the radius and \(\theta\) is the central angle in radians), which can be written as \(Sector\ Area = 0.5\times Radius^{2}\times Central\ Angle\ (in\ radians)\)

Step2: Analyze the units for area

Area is measured in square units. Meters (\(m\)) and centimeters (\(cm\)) are units of length. Degrees (\(^{\circ}\)) is a unit of angle measurement. Square centimeters (\(cm^{2}\)) is a unit of area.

Answer:

For the formula question: B. \(Sector\ Area = 0.5\times Radius^{2}\times Central\ Angle\ (in\ radians)\)
For the unit question: B. Square centimeters