By definition, the area of a circular sector is given by:
[tex]A = \frac{x\pi r^2}{360} [/tex]
Where,
r: radius of the circle
x: central angle
The central angle in degrees is given by:
[tex] x = \frac{5 \pi }{7}* \frac{180}{ \pi } = \frac{5}{7}* 180
x = 128.6[/tex]
Substituting values we have:
[tex]A = \frac{128.6*3.14*( \frac{5.6}{2} )^2}{360}[/tex]
[tex]A = 8.79[/tex]
Answer:
the area of a sector with a central angle of 5pi/7 radians and a diameter of 5.6 in is:
[tex]A = 8.79[/tex]
