Find the base radius of a cone made from a circle of a radius 12cm and length of arc 77cm

The arc length becomes the circumference of the circular base of

your cone,
so 2πr = 77
r = 77/2π = appr 12.25 cm

btw, in case there is more to the question, such as what is the
volume of the cone, the radius of 12 from your cut-out becomes the
"slant height" of your cone