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:

$S=\frac{1}{2}r^2\theta$

Where θ is the angle and r the radius.

In this case, we have:

• r = 4.28ft

,

• θ = 2.79

We write:

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

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

$S=25.55$