The radian measure of the central angle θ when the arc length is 3π cm and the radius is 10 cm is 0.3π radians.
The student is asking for the radian measure of a central angle θ in a circle, given the arc length (s) and the radius (r) of the circle.
The formula that relates the arc length, radius, and central angle in radians is θ = s / r. Given that r = 10 cm and s = 3π cm, we can find the angle by simple substitution into the formula:
θ = s / r = (3π cm) / (10 cm)
θ = 0.3π radians
This calculation shows that the central angle in radians is 0.3π when the arc length is 3π cm and the radius of curvature is 10 cm.