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The circles shown continue infinitely and have diameters 16 inches, 8 inches, 4 inches, and so on. The diameter of each circle is half the diameter of the previous circle. What is the number of square inches in the sum of the areas of all circles? Express your answer to the nearest whole number.

 

 Oct 2, 2021
 #1
avatar+35057 
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Area sequence         pi (64 + 16 +4 + 1)      the common ratio is 1/4 as you can see

sum of an infinite sequence  

S = a1 / (1-r)

 

  64 pi / (1 - 1/4 ) = 85.33 pi  in2

 Oct 2, 2021
edited by ElectricPavlov  Oct 2, 2021
 #2
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That's the wrong answer.

Guest Oct 2, 2021
 #3
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...did you multiply by the 'pi' before you just  took and ran with the numerical answer?

ElectricPavlov  Oct 2, 2021

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