Answer:
[tex]\dfrac{14\pi }{3}\ cm[/tex]
Step-by-step explanation:
The circumference of the circle with radius of 7 cm is
[tex]C=2\pi r\\ \\C=2\pi \cdot 7=14\pi \ cm[/tex]
An arc of a circle o subtends an angle of [tex]120^{\circ}[/tex] at the centre.
The circle has the full angle of [tex]360^{\circ},[/tex] then
[tex]14\pi \ cm - 360^{\circ}\\ \\x\ cm - 120^{\circ}[/tex]
Write a proportion:
[tex]\dfrac{14\pi }{x}=\dfrac{360}{120}\\ \\\dfrac{14\pi }{x}=\dfrac{3}{1}\\ \\14\pi =3x\\ \\x=\dfrac{14\pi }{3}\ cm[/tex]
