Question

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.

Answer 1

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