I am pretty sure this story dates from the 1940's or 1950's. The first lunar expedition orbits the moon and discovers it is only a façade made of wood and canvas.
Thanks to the unique image, this is likely to be the short story "Ideas Die Hard" by Isaac Asimov, originally published in the October 1957 issue of Galaxy. The store may be read online in its entirety thanks to archive.org.
It has also previously been asked about and answered here, in the question:
The unaccepted answer (by user John Rennie) to that question contains the relevant quote from the passage you recall:
But Oldbury still looked at the Moon. It was terribly close and now the surface was moving quickly. They were starting the swing in earnest and Oldbury’s scream was high-pitched. “Look! Lookathat!” His pointing finger was stiff with terror.
“You saw it. You saw the hidden side of the Moon as we went past and you saw there wasn’t any! Good Lord, just sticks, just big beams holding up six million square miles of canvas. I swear it, canvas!”