Answer:
Option B. [tex]6.75\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=3\ cm[/tex]
substitute
[tex]A=\pi (3^{2})=9 \pi\ cm^{2}[/tex]
Remember that
[tex]2\pi[/tex] radians subtends the complete circle of area [tex]9 \pi\ cm^{2}[/tex]
so
by proportion
Find the area of the related sector for a central angle of [tex]1.5[/tex] radians
Let
x------> the area of the related sector
[tex]\frac{9 \pi}{2\pi}\frac{cm^{2}}{radians} =\frac{x}{1.5}\frac{cm^{2}}{radians}\\ \\x=9*1.5/2\\ \\x= 6.75\ cm^{2}[/tex]
