Answer:
16 cm
Step-by-step explanation:
We have to first find the radius of the circle.
The area of a sector is given as:
[tex]A = \frac{\alpha }{360} * \pi r^2[/tex]
where α = central angle of the sector = 120°
r = radius of the circle
Therefore:
[tex]67 = \frac{120}{360} * \pi r^2\\\\\pi r^2 = \frac{360 * 67}{120}\\ \\r^2 = \frac{360 * 67}{120 * \pi}\\\\r^2 = 63.98\\\\r = \sqrt{63.98} = 8.0 cm[/tex]
The diameter of a circle is twice its radius, therefore:
D = 2 * 8 = 16 cm
The diameter of the circle is 16 cm
