The variable 'a' denotes the number of small circles between two big circles and the x-axis.
6
Expression 7: Start sum from "k" equals 1 to "a" , end sum, pi left parenthesis, 1 quarter , right parenthesis squared left parenthesis, StartFraction, 2 Over "k" left parenthesis, "k" plus 1 , right parenthesis , EndFraction , right parenthesis squareda∑k=1π1422kk+12
equals=
0.2 2 7 1 5 2 1 5 3 3 4 30.227152153343
7
^This is the total surface area of the small circles
8
Expression 9: left parenthesis, StartFraction, pi cubed Over 12 , EndFraction minus StartFraction, 3 pi Over 4 , EndFraction , right parenthesis minus Start sum from "k" equals 1 to "a" , end sum, pi left parenthesis, 1 quarter , right parenthesis squared left parenthesis, StartFraction, 2 Over "k" left parenthesis, "k" plus 1 , right parenthesis , EndFraction , right parenthesis squaredπ312−3π4−a∑k=1π1422kk+12
equals=
0.0 0 0 5 0 9 7 4 6 4 8 9 3 7 50.000509746489375
9
^If the number of circles was infinite, this number would be zero