Question

find the area of the smaller sector. round to the nearest tenth. area = ? ft²

Explanation:

Step1: Recall sector - area formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central - angle of the sector and $r$ is the radius of the circle.

Step2: Identify values

We are given that $\theta = 50^{\circ}$ and $r = 7.13$ ft.

Step3: Substitute values into formula

$A=\frac{50^{\circ}}{360^{\circ}}\times\pi\times(7.13)^{2}$.
First, calculate $(7.13)^{2}=7.13\times7.13 = 50.8369$.
Then, $\frac{50}{360}\times\pi\times50.8369=\frac{5}{36}\times\pi\times50.8369$.
$\frac{5}{36}\times50.8369\times\pi=\frac{254.1845}{36}\times\pi$.
$\frac{254.1845}{36}\approx7.0607$.
$7.0607\times\pi\approx7.0607\times3.14159 = 22.18$.

Step4: Round to the nearest tenth

Rounding $22.18$ to the nearest tenth gives $22.2$.

Answer:

$22.2$ ft²