What is the area of a sector with a central angle of 5pi/7 radians and a diameter of 5.6 in.? Use 3.14 for pi and round your final answer to the nearest hundredth.
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]
