Question

An arc of a circle of radius 7cm subtends an eagle of 120degree at the centre. Find its perimeter.

Answer 1

Answer:

$\dfrac{14\pi }{3}\ cm$

Step-by-step explanation:

The circumference of the circle with radius of 7 cm is

$C=2\pi r\\ \\C=2\pi \cdot 7=14\pi \ cm$

An arc of a circle o subtends an angle of $120^{\circ}$ at the centre.

The circle has the full angle of $360^{\circ},$ then

$14\pi \ cm - 360^{\circ}\\ \\x\ cm - 120^{\circ}$

Write a proportion:

$\dfrac{14\pi }{x}=\dfrac{360}{120}\\ \\\dfrac{14\pi }{x}=\dfrac{3}{1}\\ \\14\pi =3x\\ \\x=\dfrac{14\pi }{3}\ cm$