Question

Find the radius, central angle and perimeter of a sector whose length of arc and area are 4.4 m and 9.24 $m^2$ respectively.

Answer 1

Length of the arc : Area of the sector = Perimeter :Area of the circle

Then we have, $4.24:9.24=2\pi r:\pi r^2$

$=4.24:9.24=2:r$

$=4.24r=2\times 9.24$ (Product of means =product of extremes)

Then, $r=\frac{18.48}{4.24}=4.35m$

Then, the perimeter of the sector $=2\times radius+arclength=2\times 4.35+4.24=12.94$

And the central angle for the sector is :$\theta =\frac{4.24}{4.35}=0.97\approx 1\pi rad={180}^{\circ }$