The radius of a circle is 4 centimeters. What is the area of a sector bounded by a 180° arc?Give the exact answer in simplest form._____ square centimeters.

Question

asked Oct 10, 2023 41.1k views

1 Answer

Jeffrey Mixon · Answer 1 · 2023-10-17T02:07:12+0000

An area bounded by a 180° arc represents half the circle, as 180° is half the total circumference (360°).

Then, if the radius is 4 cm, we can caculate the green area as:

$\begin{gathered} A=(180)/(360)A_c=(1)/(2)A_c=(1)/(2)(\pi r^2) \\ A=(1)/(2)\pi(4)^2 \\ A=(1)/(2)\pi\cdot16 \\ A=8\pi \end{gathered}$

Answer: the area is 8π square centimeters.