we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
where
r is the radius of the circle
In this problem we have
[tex]r=9\ in[/tex]
substitute in the formula
[tex]A=\pi*9^{2}=81 \pi\ in^{2}[/tex]
The area of the complete circle subtends [tex]360\ degrees[/tex]
When the time is 4:00 the angle formed by the hands of a clock is [tex]120\ degrees[/tex]
so by proportion
Find the area of the sector area
[tex]\frac{81\pi}{360} \frac{in^{2}}{degree} =\frac{x}{120} \frac{in^{2}}{degree} \\ \\x=120*81 \pi /360\\ \\x=27 \pi\ in^{2}[/tex]
therefore
the answer is the option
[tex]27 \pi\ in^{2}[/tex]
