Answer:
Option B. [tex]212.1\ cm^{2}[/tex]
Step-by-step explanation:
step 1
Find the central angle of the shaded sector
Remember that the diameter divide the circle into two equal parts ( 180 degrees each part)
so
Let
x -----> the measure of the central angle of the shaded sector
∠x+72°=180°
∠x=180°-72°=108°
step 2
Find the area of the circle
The area of the circle is
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=15\ cm[/tex]
assume
[tex]\pi=3.1416[/tex]
substitute
[tex]A=(3.1416)(15)^{2}[/tex]
[tex]A=706.86\ cm^{2}[/tex]
step 3
Find the area of the shaded sector
Remember that the area of the complete circle subtends a central angle of 360 degrees
so
by proportion find the area of a sector by a central angle of 108 degrees
[tex]\frac{706.86}{360}=\frac{x}{108}\\ \\x=706.86*108/360\\ \\x=212.1\ cm^{2}[/tex]
