Question

A sector of 120 degree,cut out from a circle,has an area of 9sq.cm .Find the radius of the circle.

Answer 1

area of a sector of circle = πr² x angle / 360

= 3.14 x r² x 120 / 360 = 9
= 3.14 x r² x 1/3 = 9
= 3.14 x r² x 0.33 = 9
1.0362 r² = 9
and , r² = 9/1.0362
r² = 8.68
r = √8.68 = 2.94 cm ( approx 3 cm)

Answer 2

[Let theta be 'x']

Formula of sector:

  x

 ---    ×   π r²    = Area

360°

Given : theta (x) = 120° , Area = 9cm².

∴ 120°      22

   -----   ×  ----   ×  r²   = 9

   360°      7

1        22

---  ×  ----   ×  r²   = 9

3        7

                    r² = 9 × 7 × 3

                         --------------

                                 22

                     r² = 189 ÷ 22

                       r = √8.59 = 0.4

∴ The radius of the circle is 0.4cm.