Water flows through a water hose at a rate of Q$1=820$ cm$3/$s$,$ the diameter of the hose is d$1=1\mathrm{.}71$ cm$.$ A nozzle is attached to the water hose. The water leaves the nozzle at a velocity of v$2=10\mathrm{.}4$ m$/$s$.$  

Part $($a$)$  Enter an expression for the cross$-$sectional area of the hose, A$1,$ in terms of its diameter, d$1.$  

Part $($b$)$  Calculate the numerical value of A$1,$ in square centimeters. 

Part $($c$)$  Enter an expression for the speed of the water in the hose, v$1,$ in terms of the volume flow rate Q$1$ and cross$-$sectional area A$1.$  

Part $($d$)$  Calculate the speed of the water in the hose, v$1$ in meters per second.