$6$ a$)[8$ marks$$ A $50-$liter bucket is filled using a garden hose attached with a nozzle. The inner diameter of the hose is $2\mathrm{.}5$ cm and is reduced to $1\mathrm{.}25$ cm at the exit of the nozzle. If the average velocity in the hose is $\backslash (2\mathrm{.}5\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ),$ determine $($i$)$ the volume and mass flow rates of water through the hose, $($ii$)$ how long it will take to fill the bucket with water, $($iii$)$ the average velocity of water at the exit of the nozzle, and $($iv$)$ if the existing nozzle is replaced by one with exit diameter of $0\mathrm{.}5$ cm $,$ will the bucket fill faster or slower?