Question

For an arch length s, area of sector A, and central angle θ of a circle of radius r, find the indicated quantity for the given value. r=4.28 ft, θ= 2.79, s=?

Answer 1

The area of a sector S follows the equation:

`S=(1)/(2)r^2\theta`

Where θ is the angle and r the radius.

In this case, we have:

• r = 4.28ft

,

• θ = 2.79

We write:

`\begin{gathered} S=(1)/(2)(4.28)^2\cdot2.79 \\ S\approx25.554168 \end{gathered}`

Then, the answer, rounded up to two decimal places is

`S=25.55`