Area of the Sector

Note: Threads given without a section number are from the David Cohen textbook. This is done to make a distinction between the books.

1. What is the needed formula?
2. Can you do 23 (a & b)?

 

23.
a.
The formula for the area of a sector is:

A = r^2* (θ / 2)

A = 6^2 * (2pi/3) / 2
A = 36* pi/3
A =37.6991cm^2

b.
r=5m, θ=80 degrees =>which is equal to

A = 5^2* ((4pi/9) / 2)
A = 5^2* (2pi/9)
A =17.453m^2

 

Let me see. Theta must be in radian measure for this type of question. Yes? If so, why must theta be in radian measure? Why not in degrees?

 

you can use either degrees or radians:

Area of a Sector of Circle = (θ/360º) × πr^2, where, θ is the angle subtended at the center, given in degrees, r is the radius of the circle.
Area of a Sector of Circle = 1/2 × r^2θ, where, θ is the angle subtended at the center, given in radians, r is the radius of the circle.

 

Thanks.