Radii and other measures of length can be in any form of number (other than complex or negative values) and can have any unit of measure (as long as it's a measure of length, rather than volume or something). There is no requirement that a radius be stated in terms of $\displaystyle \pi$.

When no calculator is allowed, they should not, in my opinion, be wasting your time asking you to do the long division of 360 by the decimal approximation 3.14 (or whatever value they'd specified) to convert the angle measure to degrees.

But that's the way you'd do the conversion: Divide 360 by 3.14:

Code:

long division:
114
------
314 )36000
314
------
4600
314
------
1460
1256
------
204

So you've got $\displaystyle 114\frac{102}{157}^\circ$.

Whether or not you want to continue on to get the decimal degrees or else the "minutes" and "seconds" is up to you.