That big drum looking thingy on the rear of the turret is the ammo bin. Same as the A-10.
Thing about Air Defence engagements is, you are not going to be firing a-la hollywood at masses of incoming targets. Think of missile systems, the most they have is 8 before reloading, so, 8 engagements before the ammo truck comes up and does a resup.
Even a twin 35 only has enough ammo for maybe 8-10 combat bursts of 2.5 seconds each. If you're in a short range AD vehicle and engaging more than 10 aircraft in between resupply opportunities, then something has gone horribly wrong with the theatre air defence plan.
In my ADATS troop, although we carried 8 missiles per system, we would have to request permission to expend more than 6 per day. Granted, missile resupply can easily become a strategic issue compared to 35mm rounds, hence the daily expenditure cap.
All that to say I ain't gonna add a ginormous ammo hopper to muh tank.