Question

1. Find the area of the shaded sector.
2. Find the length of the arc defined by the sector.

Answer 1

1. 150π sq.ft 2. 10π ft

Explanation:

Part 1

Equation: Area of a sector =
`(x)/(360)` × π
`r^(2)`

Where:

x = internal angle

r = radius of circle

Values from problem:

x = 60

r = 30

Plug values into equation:

Area of sector =
`(60)/(360)` × π
`30^(2)`

Simplify:

60 divided by 30 equals
`(1)/(6)` and 30 squared equals 900 so...

`(1)/(6)` × 900π

900π divided by 6 equals 150π so...

`(900)/(6)` × π = 150π

150π sq. ft

Part 2

Equation: Arc length =
`(x)/(360)` × 2πr

Where:

x = internal angle

r = radius of circle

Values from Problem:

x = 60

r = 30

Plug values into equation:

Arc length =
`(60)/(360)` × 2π30

Simplify:

60 divided by 360 equals
`(1)/(6)`, and 2π × 30 equals 60π so...

`(1)/(6)` × 60π

60π divided by 6 is 10π

`(60)/(6)`π = 10π

10π ft