1. A system for measuring a volume of a ballonet, the system comprising: a plurality of reflectors arranged in a grid pattern along a non-rigid interior surface of the ballonet and configured to reflect a plurality of signals directed at the plurality of reflectors; a plurality of sensors mounted on a rigid interior surface of the ballonet and configured to transmit the plurality of signals toward the non-rigid interior surface of the ballonet and to receive the plurality of signals reflected off of the plurality of reflectors while the ballonet is not fully pressurized and comprises a folded, wrinkled or creased portion of the non-rigid interior surface of the ballonet; and one or more processors configured to: calculate, while the ballonet is not fully pressurized and comprises the folded, wrinkled or creased portion of the non-rigid interior surface of the ballonet, a plurality of distances from the plurality of sensors to the plurality of reflectors using the received-plurality of signals; create a three-dimensional surface using the calculated plurality of distances; and calculate the volume of the ballonet using the three-dimensional surface.