Expression 15: Start integral from 0 to "h" , end integral, pi left parenthesis, left parenthesis, negative StartFraction, "z" "r" Over "h" , EndFraction positive "r" , right parenthesis squared minus 0 squared , right parenthesis "d" "z" equals 157.0 7 9 6 3 2 6 7 9∫h0π−zrh+r2−02dz
equals=
157.0 7 9 6 3 2 6 7 9157.079632679
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Volume by Integration (Shells)
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Expression 17: Start integral from 0 to "r" , end integral, 2 pi "x" left parenthesis, left parenthesis, negative StartFraction, "h" Over "r" , EndFraction "x" plus "h" , right parenthesis minus 0 , right parenthesis "d" "x" equals 157.0 7 9 6 3 2 6 7 9∫r02πx−hrx+h−0dx
equals=
157.0 7 9 6 3 2 6 7 9157.079632679
17
Surface Area
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18
Surface Area by Formula
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Expression 20: pi "r" left parenthesis, "r" positive StartRoot, "h" squared positive "r" squared , EndRoot , right parenthesis equals 201.2 2 2 9 3 1 3 6 2πrr+h2+r2
equals=
201.2 2 2 9 3 1 3 6 2201.222931362
20
Surface Area by Integration (Rings)
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Expression 22: Start integral from 0 to "h" , end integral, 2 pi left parenthesis, negative StartFraction, "z" "r" Over "h" , EndFraction positive "r" , right parenthesis StartRoot, left parenthesis, negative StartFraction, "r" Over "h" , EndFraction , right parenthesis squared positive 1 , EndRoot "d" "z" positive Start integral from 0 to "r" , end integral, 2 pi "x" "d" "x" equals 201.2 2 2 9 3 1 3 6 2∫h02π−zrh+r−rh2+1dz+∫r02πxdx
equals=
201.2 2 2 9 3 1 3 6 2201.222931362
22
Perspective View
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23
Expression 24: theta Subscript, "h" "o" "r" "i" "z" "o" "n" "t" "a" "l" , Baseline equals negative 0.5θhorizontal=−0.5
