Area of the Sector

[nycmathguy]

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)?

 

[MathLover1]

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

 

[nycmathguy]

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?

 

[MathLover1]

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.

 

[nycmathguy]

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.