An arc on a circle that is 18 cm long, subtends a 28.8° angle at the centre. What is the circumference of the circle?

225 cm

Length of arc = 18 cm

Angle subtended by arc at center = 28.8º

Angle is in degree , to convert into radian

= 28.8 × \(\frac{ π }{180}\)

=  0.16 × π

We know that ,

Radius = \(\frac{ Arc }{Angle}\)

= \(\frac{ 18 }{ 0.16 × π }\)

= \(\frac{ 112.5 }{ π }\)

Now,

Circumference of the circle = 2 × π × r

= 2 × π × \(\frac{ 112.5 }{ π }\)

= 225 cm