Area of sector

Question

Find the area of the sector of the circle of the central angle ∅=320° and radius r=8.9

A. 1424.0 cm^2

B. 24.85 cm^2

C. 12673.6 cm^2

D. 221.20 cm^2

E. None

Answer 1

First, draw a circle with radius 8.9 cm.
 
Then, mark the arc from 0° to 320° (roughly is o.k.).  That is 320/360-ths of the area of the entire circle.
 
The area of the entire circle (A=πr²) is:  A = π(8.9)²  cm² = 79.21π cm².
 
3200/360-ths of (note: the word "of" usually means multiply) the area of the circle is:
     (320/360)*(79.21)*π cm²
      70.41π cm²
       221.20 cm² (rounded)

Answer 2

Since a full circle is 360º, we can treat the 320° portion as a fraction of the full area. Simply multiply the area by 320/360:

320/360 · π·(8.9)² = 221.20 cm² (Option D)