A circle with area 36 pi has a sector with central angle of f 11/6 pi radians

33 π

Step-by-step explanation:

Given,

Area of circle = 36 π

Central angle of sector,θ = 11/6 rad

Area of the sector = ?

we know,

A = π r²

36 π = π r²

r = 6

Area of sector

8.57°91.5 feet13.68 feet 625.93 ft²1723.86 feet

Step-by-step explanation:

1. The circle is divided by 42 equal sectors.

Each sector has angle of:

360°/42 = 8.57° (rounded)

2. The radius is half of the diameter:

r = d/2 = 183 /2 = 91.5 feet

3. The length of the circle is:

C = 2πr = 2*3.14*91.5 = 574.62 feet

Each arc has the length of:

574.62/42 = 13.68 feet (rounded)

4. Area of each sector is:

A = πr²/42 = 3.14*91.5²/42 = 625.93 ft² (rounded

5. 3 revolutions is equal to 3 times the perimeter of circle (take from question 3) :

3*574.62 feet = 1723.86 feet