What was found
TAXI CHECKS AND DEPARTURE WERE ALL UNEVENTFUL. CREW WAS CLIMBING TO FL450 AND PASSING THROUGH FL400 WHEN THEY RECEIVED A "HYDRAULIC VOLUME LOW A" AMBER CAUTION MESSAGE. THEY COMPLETED THE CHECKLIST AND SLACKED A MESSAGE TO MAINTENANCE CONTROL ABOUT THE ISSUE. REVIEWING THE CHECKLIST FOR A HYDRAULIC SYSTEM A FAILURE. CREW DECLARED AN EMERGENCY TO RECEIVE PRIORITY HANDLING AND ADVISED ATC THAT WE MAY NOT BE ABLE TO CLEAR THE RUNWAY. THE APPROACH, LANDING, AND SUBSEQUENT ROLLOUT WENT ACCORDING TO PLAN. THEY CLEARED RWY ALTHOUGH THEY ONLY HAD ENOUGH STEERING AND BRAKING TO CLEAR ONTO A MIDFIELD TAXIWAY. FIRE RESCUE AS WELL AS AIRPORT OPS COMPLETED A CHECK OF THE RUNWAY AND AIRCRAFT. ALL WAS CLEARED EVEN THOUGH IT WAS LATER DISCOVERED THAT THE AIRCRAFT WAS LEAKING A LITTLE HYDRAULIC FLUID THROUGH THE TAIL CONE DOOR.