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 = (x\pi r^2)/(360)`
Where,
r: radius of the circle
x: central angle
The central angle in degrees is given by:

`x = (5 \pi )/(7)* (180)/( \pi ) = (5)/(7)* 180 x = 128.6`
Substituting values we have:

`A = (128.6*3.14*( (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`