Final answer:
The radius of the circle is 70 units, calculated by dividing the arc length (35 π/3) by the angle in radians (1 π/6).
Step-by-step explanation:
To find the radius of the circle given an angle in radians and the arc length it intercepts, we use the formula arc length = radius × angle in radians. Here, the angle is given as 1 π/6 radians and the arc length is 35 π/3. By rearranging this formula to solve for the radius (r), we get r = arc length / angle.
Therefore, the radius (r) of the circle is:
r = (35 π/3) / (1 π/6)
r = (35 π/3) × (6/π)
r = 70
Thus, the radius of the circle is 70 units in simplest form.