I took my geiger counter on a flight once just out of interest to measure the radiation inflight. It was around 20 times ground level at about 23,000 feet.
As has already been mentioned, the plane’s skin provides little to no shielding particularly higher energy particles which come from outer space.
Aluminium for example will only stop x-rays in the lower end of that band (soft x-rays). Hard x-rays (higher energy) and above including gamma will sail straight through.
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