Infinity

In a square with side 19 is inscribed circle, the circle is inscribed next square, again circle, and so on to infinity. Calculate the sum of the area of all these squares.

Correct answer:

S =  722

Step-by-step explanation:

a1=19 S1=a12=192=361 d1=a1=19 d1=2a2  a2=d1/2=19/213.435 S2=a22=13.4352=2361=18021=180.5  q=S2/S1=180.5/361=21=0.5  S=S1 1q1=361 10.51=722   Verifying Solution:  d2=a2=13.43513.435 d2=2a3  a3=d2/2=13.435/2=219=921=9.5 S3=a32=9.52=4361=9041=90.25  q2=S3/S2=90.25/180.5=21=0.5



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Showing 2 comments:
Ann
I don't believe this answer is correct. The ratio (q) to find the area of the next square should be 1/8, not 1/2.

Math student
no it is 1/2





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