I have a question, and I cannot figure out why my theory does not work.

Say we have a circle tablecloth with 48 inch diameter.

This clearly has an area of 576 pi.

Now let's say this same tablecloth is put over a 36 inch table. It now takes the shape of a cylinder without a bottom, with a height of six inches on each side and a diameter of 36. So why does the modified cylinder formula [2(pi)(18)(6) + pi(18)^2] not equal the same area of 576 pi, but a lesser 540 pi?

Say we have a circle tablecloth with 48 inch diameter.

This clearly has an area of 576 pi.

Now let's say this same tablecloth is put over a 36 inch table. It now takes the shape of a cylinder without a bottom, with a height of six inches on each side and a diameter of 36. So why does the modified cylinder formula [2(pi)(18)(6) + pi(18)^2] not equal the same area of 576 pi, but a lesser 540 pi?

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