Question

Consider a sector with angle `pi/3` radians, and radius `3.5 m`. What is the arc length and area?

Answer 1

Sector length `= 7/6pi = 3.67 \ m` (2dp)

Area `=49/24 pi = 6.41 \ m^2` (2dp)

Explanation:

The sector length when the angle is measured in radians is

`l = r theta`

So in this case:

`l = (3.5) * pi/3`
`\ \= 3.66519 ...`

And the Area is given by:

`A = 1/2r^2 theta`

So in this case:

`A = 1/2 (3.5)^2 pi/3`
`\ \ \ = 49/24 pi`
`\ \ \ = 6.414085 ...`