Question

find the area of a sector with a central angle of 170° and a radius of 17 millimeters. round to the nearest tenth. 857.5 mm² 100.9 mm² 428.7 mm² 25.2 mm²

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 measure in degrees and $r$ is the radius of the circle.

Step2: Substitute the given values

We are given that $\theta = 170^{\circ}$ and $r = 17$ mm. Substitute these values into the formula: $A=\frac{170^{\circ}}{360^{\circ}}\times\pi\times(17)^{2}$.

Step3: Calculate the area

First, $(17)^{2}=289$. Then, $\frac{170}{360}\times\pi\times289=\frac{17}{36}\times\pi\times289$.
$A=\frac{17\times289\pi}{36}=\frac{4913\pi}{36}\approx\frac{4913\times3.14159}{36}$.
$4913\times3.14159 = 4913\times(3 + 0.1+0.04 + 0.001+0.0005 + 0.00009)=14739+491.3+196.52+4.913+2.4565+0.44217 = 15434.63167$.
$A=\frac{15434.63167}{36}\approx428.7$ $mm^{2}$.

Answer:

$428.7$ $mm^{2}$