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A restaurant is remodelling and replacing its circular tables with square tables. They want the new tables to have the same area as the old ones. The circumference of the circular tables is measured to be 4.1m. Find the side length of the new square tables

 

i) To an appropriate degree of accuracy

 Jun 26, 2019
 #1
avatar+104704 
+2

Circumference  =  2 pi * r

 

4.1  =  2 pi * r       divide both sides by 2pi

 

4.1 / [ 2pi]  = r

 

So....the area of one table is just the area of a circle  =  pi  r^2  =   pi *  [  4.1 / [2pi]  ]^2  =

 

 [ 4.1 / 2] ^2 / pi    m^2

 

And this is equal to the area of the square

 

So....the side of this square is just the square root of this  =  [ 4.1/2] / pi^(1/2) ≈  1.16 m

 

 

cool cool cool

 Jun 26, 2019
 #2
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+1

Wow, thanks for responding so quickly but unfortunately the answer is 7.3m instead of 1.16m and I'm not sure why it is, the text book only reveals the answer instead of a methodical guide. 

Guest Jun 26, 2019
 #3
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+1

 

I hate to be the one to tell the textbook people they're wrong, but they're wrong.

 

I worked it myself, and CPhill is right on the money.  The side of each table is 1.16 meter.

 

Just think about it.  Every table is 7.3 meters square?  Every table is 24 FEET wide?  I don't think so. 

 

Check and see if you accidentally looked at the wrong answer in the textbook.

.

Guest Jun 26, 2019
edited by Guest  Jun 26, 2019
 #4
avatar+104704 
+2

Consider...if the side of the square is 7.3 m....the area   = 7.3^2  = 53.29 m^2

 

So......this is equal to the area of one of the circular tables

 

So.....

 

53.29  = pi * r^2

 

53.29/pi =  r^2       take the square root of both sides

 

r ≈  4.1 m

 

I'm wondering if this  was meant in the original problem instead of  a circumference of 4.1  m  ???

 

 

cool cool cool

CPhill  Jun 26, 2019
edited by CPhill  Jun 26, 2019
 #5
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+1

 

CPhill, your observation is certainly persuasive.  The numbers come out right.  But still... when was the last time you were in a restaurant where the tables were 8.2 meters across?  27 feet across!  Even King Arthur's wasn't that large.   

.

 Jun 26, 2019

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