A designer draftsperson must draw a pan lid in circular form. To perform this drawing, she has, at the moment, only a compass whose leg length is 10 cm, a protractor, and a sheet of paper with a Cartesian plane. To sketch this lid, she separated the compass legs so that the angle formed by them was $120^{\circ}$. The needle point is represented by point $C$, the pencil point is represented by point $B$, and the compass head is represented by point $A$.
After completing the drawing, she sends it to the production department. Upon receiving the drawing with the indication of the lid's radius, they will verify in which interval it falls and decide the type of material to be used in its manufacture, according to the data.
| Type of material | Interval of radius values (cm) |
| I | $0 < \mathrm{R} \leq 5$ |
| II | $5 < \mathrm{R} \leq 10$ |
| III | $10 < \mathrm{R} \leq 15$ |
| IV | $15 < \mathrm{R} \leq 21$ |
| V | $21 < \mathrm{R} \leq 40$ |
Consider 1.7 as an approximation for $\sqrt{3}$. The type of material to be used by the production department will be
(A) I.
(B) II.
(C) III.
(D) IV.
(E) V.