a circle with radius 3 has a sector with a central angle of 17/9 pi radians. what is the area of the sector?

The area of the sector is 26.69

Step-by-step explanation:

First of all we need to calculate the area

To solve this problem we need to use the area formula of a circle:

a = area

r = radius = 3

π = 3.14

a = π * r²

we replace with the known values

a = 3.14 * (3) ²

a = 3.14 * 9

a = 28.26

The area of the circle is 28.26

A complete circle has 2pi radians

We divide 17/9 pi by 2pi and obtain the fraction of the total circle

(17pi/9) / 2pi = 17/18

we multiply this fraction with the area of the circle and obtain the area of the sector

28.26 * 17/18 = 12.43cm

The area of the sector is 26.69