If the circumference of a circle is 64 cm what is the length of an arc that measures 30 degrees .

The circumference of a circle is  given by the formula 2pi*r
.

The actual length of the cicumference =
64.

Therefore  2pir = 64 cm.

An angle
of 30 degrees = pi/6 radians.

Therefore the length of an arc which
subtends an angle of x radians at the centre should measure x*radius =
xr.

Therefore an arc subtending pi/6 radians should measure
pi*r/6.

But 2pir = 64 cm given.

Divide
both sides by 12 :

2pir/12 =
64/12.

Therefore pir/6 = 64/12 cm  = 5 1/3
cm

Therefore an arc angle of 30 degrees of a circle whose
circumference is 64 measure 5 1/3 cm or 5.33cm nearly.