A motor shaft is being designed to transmit $40 \mathrm{kW}$ of power at $900 \mathrm{rpm}$. If the shearing stress in the shaft must be limited to $75 \mathrm{MPa}$, determine:

a) the minimum diameter required for a solid shaft.

b) the minimum outside diameter required for a hollow shaft if the shaft inside diameter is assumed to be $80\%$ of its outside diameter.