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A piece of wire 72 cm long is cut into two equal pieces and each is formed into a circle. What is the sum, in square centimeters, of the areas of these circles?

 Mar 14, 2021
 #1
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206.2648 cm^2 total

103.1324 cm.^2 for each circle

-baljeet

 Mar 14, 2021
 #3
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I'm sure the OP appreciates your going into such detail, indianguy.  You explained it so well.  

Guest Mar 14, 2021
 #2
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A piece of wire 72 cm long is cut into two equal pieces and each is formed into a circle. What is the sum, in square centimeters, of the areas of these circles?     

 

Figure the area of one circle then double it. 

 

One circle has a circumference of 36. 

 

Circumference  =  diameter • π  =  2 • radius • π  

 

                       36  =  2 • r • π  

 

                         r  =  36 / 2π   =  18 / π  

 

                         Area  =  π • r2   

 

                         Area  =  π • (18 / π )2  

 

                         Area  =  π • 182 / π2  

 

                         Area  =  182 / π  

 

It's time to substitute the value of pi ..... let's call it 3.1416  

 

                         Area  =  324 / 3.1416  =  103.13         rounded to 2 decimal places   

 

                         Area of two circles this size  =  2 • 103.13  =  206.26 cm2   

 

.

 Mar 14, 2021

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