A circular piece of wire has a radius of 12 cm. This is cut then bent to form an arc of a circle whose radius is 60 cm. Find the angle subtended at the centre by this arc. Give your answer to the nearest degree.

Question

Please show working out
Thank you so much!

Answer 1

the circumference of the original circle becomes the arc length of the sector.
circumf. of circle = 2πr = 24π

arc = rØ, were Ø is the central angle in radians and r is the radius
so if r = 60
60Ø = 24π
Ø = 24π/60 radians = 2π/5 radians

I know π/5 radians = 36° , so
2π/5 radians = 72°