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The side of a square  a = 2cm ( a = r ).  Find the areas of:  X, Y and Z.

 

 

Image result for area of 4 quarter circles in a square

civonamzuk  May 23, 2015

Best Answer 

 #1
avatar+78551 
+8

 

 

Using some calculus  (and symmetry), we have  

 z = (in sq cm)             

 

I'll use a more exact value = 0.1735540900379272 sq cm.

           

And solving some equations, we have

 

4 - pi = y + 2z   →   y = 4 - pi - 2z  = 4 - pi - 2(0.1735540900379272) ≈ 0.5112991663343523615  sq cm

 

And

 

x + 3y + 2z = pi  →     x = pi - 3y - 2z =  

pi - 3(0.5112991663343523615) - 2( 0.1735540900379272)

≈  1.2605869745108817539626  sq cm

 

Check

 

x + 4y + 4z = 4  ???

 

1.2605869745108817539626+ 4(0.5112991663343523615 )+ 4(0.1735540900379272) =

 

3.9999999999999999999626  sq cm

 

Close enough  !!!!

 

 

CPhill  May 23, 2015
Sort: 

1+0 Answers

 #1
avatar+78551 
+8
Best Answer

 

 

Using some calculus  (and symmetry), we have  

 z = (in sq cm)             

 

I'll use a more exact value = 0.1735540900379272 sq cm.

           

And solving some equations, we have

 

4 - pi = y + 2z   →   y = 4 - pi - 2z  = 4 - pi - 2(0.1735540900379272) ≈ 0.5112991663343523615  sq cm

 

And

 

x + 3y + 2z = pi  →     x = pi - 3y - 2z =  

pi - 3(0.5112991663343523615) - 2( 0.1735540900379272)

≈  1.2605869745108817539626  sq cm

 

Check

 

x + 4y + 4z = 4  ???

 

1.2605869745108817539626+ 4(0.5112991663343523615 )+ 4(0.1735540900379272) =

 

3.9999999999999999999626  sq cm

 

Close enough  !!!!

 

 

CPhill  May 23, 2015

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