Question

Calculate the radius of segment of length20cm which subtend at angle 120 degree leave your answer to the nearest whole number take pie 22/7

Answer 1

when you say a segment of length 20, is that the chord length or the arc length?

in any case, se the related problems below.

Answer 2

120° / 360° = 120° ∙ 1 / 120° ∙ 3 = 1 / 3

The circumference of circle:

C = 2 r π

Segment which subtend at angle 120° have lenght of one third of circumference.

C / 3 = 20 cm

2 r π / 3 = 20

Multiply both sides by 3

2 r π = 60

Divide both sides by 2 π

r = 60 / 2 π

r = 30 / π = 30 / ( 22 / 7 ) = 30 ∙ 7 / 22 = 210 / 22 = 9.5454...

r = 10 cm

rounded to the nearest whole number

Answer 3

Your question is ambiguous.
Bosnian assumed that the 20 cm referred to the arc length.
This assumption makes sense, since you mention using π.

One could also assume that the 20 cm refers to the length
of the chord, if so ....

simplest way:
you have an isosceles triangle with base angles of 30° each .
By the sine law:
r/sin30 = 20/sin120
r = 20sin30/sin120 = appr 11.55 cm

btw, this is 2022. If your text suggests using 22/7 for π, it is time to
replace that medieval text. Every decent calculator has the value of
π installed as a constant.