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?
Answer & explanation
Correct answer: option 3
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