Please help. A very tough math concept I cannot wrap my head around

Jun 2015
8
0
Long Island
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?
 
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v8archie

Math Team
Dec 2013
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2,682
Colombia
Because it's not a cylinder, the sides don't hand straight down.
 
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greg1313

Forum Staff
Oct 2008
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London, Ontario, Canada - The Forest City
Think about what happens to the circumference of the table cloth.
 

CRGreathouse

Forum Staff
Nov 2006
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UTC -5
This is a good question, and I really like the thought process you used to come up with it. I think both of the answers are helpful in giving you the right intuition here. Good luck!
 
May 2015
109
5
Varanasi
You mentioned that it will become a cylinder with no bottom, the formula which you are using is for closed cylinder's area, but your cylinder is open at one base.This means from the expression you must subtract the area of the circular part of the table.
 

Denis

Math Team
Oct 2011
14,592
1,026
Ottawa Ontario, Canada
Well, you could always cut a 36d-circle from your 48d-tablecloth,
then play with the 6wide ring leftover...
perhaps practice throwing it so it rings around the microwave oven...

Got a better idea, Archie?