Answer:
[tex]A=28.1\ cm^2[/tex]
Step-by-step explanation:
The area of a circular sector with a central angle θ and radius r is given by:
[tex]\displaystyle A=\frac{1}{2}r^2 \theta[/tex]
Note: The angle must be in radians.
We need to find both the radius and the angle in radians.
Diameter = 9.6 cm
Radius r=Diameter/2=4.8 cm
Angle in radians= Angle in degrees*π / 180
θ = 140*π / 180 = 2.4435 rad
Now we calculate the area:
[tex]\displaystyle A=\frac{1}{2}(4.8)^2 2.4435[/tex]
[tex]\boxed{A=28.1\ cm^2}[/tex]
