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Expression 6: "h" left parenthesis, "x" , right parenthesis equals left brace, "x" less than or equal to 2 "r" : StartRoot, "r" "r" minus left parenthesis, "x" minus "r" , right parenthesis squared , EndRoot , "x" less than or equal to 2 "R" : 0 , right brace

6

Expression 7: "y" equals "r" left brace, "g" left parenthesis, "r" , right parenthesis less than or equal to "x" less than or equal to 2 times "R" minus "g" left parenthesis, "r" , right parenthesis , right brace

7

Expression 8: "D" equals 2 "R" minus 2 "g" left parenthesis, "r" , right parenthesis

equals

24

8

Expression 9: "r" equals StartRoot, "R" times "R" minus 12 squared , EndRoot

0

domain \theta Minimum:

less than or equal to theta less than or equal to

12 pi

domain \theta Maximum:

equals

25.4 4 2 0 3 0 1 8 6 3

9

${D} left parenthesis, "R" , "r" plus 1 , right parenthesis

Label:

10

${A}pi left parenthesis, "r" plus "R" , 2 , right parenthesis

Label:

11

Expression 12: "A" equals StartFraction, 1 Over pi , EndFraction Start integral from 0 to 2 "R" , end integral, left parenthesis, "f" left parenthesis, "x" , right parenthesis minus "h" left parenthesis, "x" , right parenthesis , right parenthesis "d" "x"

equals

72

12

13

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