In the peom concrete mixer I didn't understand what is meant by they rid the trunk like trough of concrete.

Concrete Mixers deliver concrete down a movable trough to where it is being used. That trough has to be cleaned at the end, or the residual concrete will end up clogging the future flows...very much the same as in you, when you have a stuffy nose. She is comparing the trough to an elephant's nose.