A certain hydraulic system is designed to exert a force $272$ times as large as the one put into it$.$

$($a$)$

What must be the ratio of the area of the slave cylinder to the area of the master cylinder?

AslaveAmaster

$=$

$($b$)$

What must be the ratio of their diameters?

DslaveDmaster

$=$

$($c$)$

By what factor is the distance through which the output force moves reduced relative to the distance through which the input force moves? Assume no losses to friction.

doutput

$=$

dinput