Expression 8: 0.7 4 times StartFraction, left parenthesis, "D" Subscript, "h" "o" "l" "l" "o" "w" , Baseline minus 2 "T" , right parenthesis cubed Over "D" cubed , EndFraction0.74·Dhollow−2T3D3
equals=
1568.0 3 2 9 2 2 11568.0329221
8
Size comparison of solid and hollow discs (scroll out to see)
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9
Expression 10: "D" Subscript, "d" "o" "n" "u" "t" , Baseline equals StartFraction, "D" squared plus 4 "T" squared Over 4 "T" , EndFractionDdonut=D2+4T24T
equals=
19602081960208
10
Expression 11: "r" equals StartFraction, "D" Subscript, "d" "o" "n" "u" "t" , Baseline Over 2 , EndFraction minus left bracket, 0 , "T" , right bracketr=Ddonut2−0,T
00
domain \theta Minimum:
less than or equal to theta less than or equal to≤θ≤
2 pi2π
domain \theta Maximum:
equals=
980104980104
980096980096
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You could fit around these many solid discs inside the donut
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Expression 13: StartFraction, pi Over 2 StartRoot, 3 , EndRoot , EndFraction times StartFraction, left parenthesis, "D" Subscript, "d" "o" "n" "u" "t" , Baseline minus 2 "T" , right parenthesis squared Over "D" squared , EndFractionπ23·Ddonut−2T2D2
equals=
55552.8 2 0 2 0 3 855552.8202038
13
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14
Expression 15: "r" less than or equal to StartFraction, "D" Over 2 , EndFractionr≤D2
00
domain \theta Minimum:
less than or equal to theta less than or equal to≤θ≤
