Question

Find the approximate area of the sector shown. Answer to the nearest hundredth of a square inch. Use your calculator value of .5 in.5 in.80°A circle contains two line segments, an unlabeled point, two lengths, an angle, and a shaded region.The first segment starts at the center point of the circle, goes up and ends at the top of the circle. It is labeled 5 inches.The second segment starts at the center point of the circle, goes up and right and ends slightly above the center right of the circle. It is labeled 5 inches.The angle at the center point of the circle to the right of the first segment and above the second segment is labeled 80°.The area to the right of the first segment and above the second segment in the interior of the circle is shaded. in2

Answer 1

ANSWER :

17.45 in^2

EXPLANATION :

Recall the area formula of a segment :

$A=\pi r^2\times\frac{\theta}{360}$

where r = radius and θ = central angle.

From the problem, the radius is 5 inches and the central angle is 80 degrees.

Using the formula above :

$\begin{gathered} A=\pi(5)^2\times\frac{80}{360} \\ A=17.45in^2 \end{gathered}$