Water flows through a water hose at a rate of \(Q_{1}=680cm^{3}/s\), the diameter of the hose is \(d_{1}=2.2cm\). A nozzle is attached to the water hose. The water leaves the nozzle at a velocity of \(v_{2}=9.2m/s\).

a) Enter an expression for the cross-sectional area of the hose, \(A_{1}\), in terms of its diameter, \(d_{1}\)

b) Calculate the numerical value of \(A_{1},\) in square centimeters.

c) Enter an expression for the speed of the water in the hose, \(v_{1}\), in terms of the volume floe rate \(Q_{1}\) and cross-sectional area \(A_{1}\)

d) Calculate the speed of the water in the hose, \(v_{1}\) in meters per second.

e) Enter an expression for the cross-sectional area of the nozzle, \(A_{2}\), in terms of \(v_{1},v_{2}\) and \(A_{1}\)

f) Calculate the cross-sectional area of the nozzle, \(A_{2}\) in square centimeters.