Answer:
1. 150π sq.ft 2. 10π ft
Step-by-step explanation:
Part 1
Equation: Area of a sector = [tex]\frac{x}{360}[/tex] × π[tex]r^{2}[/tex]
Where:
x = internal angle
r = radius of circle
Values from problem:
x = 60
r = 30
Plug values into equation:
Area of sector = [tex]\frac{60}{360}[/tex] × π[tex]30^{2}[/tex]
Simplify:
60 divided by 30 equals [tex]\frac{1}{6}[/tex] and 30 squared equals 900 so...
[tex]\frac{1}{6}[/tex] × 900π
900π divided by 6 equals 150π so...
[tex]\frac{900}{6}[/tex] × π = 150π
150π sq. ft
Part 2
Equation: Arc length = [tex]\frac{x}{360}[/tex] × 2πr
Where:
x = internal angle
r = radius of circle
Values from Problem:
x = 60
r = 30
Plug values into equation:
Arc length = [tex]\frac{60}{360}[/tex] × 2π30
Simplify:
60 divided by 360 equals [tex]\frac{1}{6}[/tex], and 2π × 30 equals 60π so...
[tex]\frac{1}{6}[/tex] × 60π
60π divided by 6 is 10π
[tex]\frac{60}{6}[/tex]π = 10π
10π ft
