A rectangular key was used to connect the pulley connected to the line shaft transmitting a power of $10$ hp at a speed of $1200$ rpm$.$ What is the diameter of the shaft considering that the shearing stress of the shaft and key are $30$ MPa and $240$ MPa respectively?

A$.11\mathrm{.}6$ mm

B$.21\mathrm{.}6$ mm

C$.15\mathrm{.}6$ mm

D$.7\mathrm{.}81$ mm

The correct answer is $21\mathrm{.}6$ mm$,$ please justify. Thank you!