Expression 14: 1 third pi "h" left parenthesis, "r" squared positive "r" "R" positive "R" squared , right parenthesis13πhr2+rR+R2
equals=
205.2 5 0 7 2 0 0 3 5205.250720035
14
Volume by Integration (Discs)
15
Expression 16: Start integral from 0 to "h" , end integral, pi left parenthesis, left parenthesis, negative StartFraction, "R" negative "r" Over "h" , EndFraction "z" positive "R" , right parenthesis squared minus 0 squared , right parenthesis "d" "z"∫h0π−R−rhz+R2−02dz
equals=
205.2 5 0 7 2 0 0 3 5205.250720035
16
Volume by Integration (Shells)
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Expression 18: Start integral from 0 to "r" , end integral, 2 pi "x" left parenthesis, "h" minus 0 , right parenthesis "d" "x" positive Start integral from "r" to "R" , end integral, 2 pi "x" left parenthesis, StartFraction, "h" left parenthesis, "R" negative "x" , right parenthesis Over "R" negative "r" , EndFraction negative 0 , right parenthesis "d" "x"∫r02πxh−0dx+∫Rr2πxhR−xR−r−0dx
equals=
205.2 5 0 7 2 0 0 3 5205.250720035
18
Surface Area
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19
Surface Area by Formula
20
Expression 21: pi left parenthesis, "R" positive "r" , right parenthesis StartRoot, left parenthesis, "R" negative "r" , right parenthesis squared positive "h" squared , EndRoot positive pi "r" squared positive pi "R" squaredπR+rR−r2+h2+πr2+πR2
equals=
219.2 1 1 1 8 5 9 1 9219.211185919
21
Surface Area by Integration (Rings)
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Expression 23: Start integral from 0 to "h" , end integral, 2 pi left parenthesis, negative StartFraction, "R" negative "r" Over "h" , EndFraction "z" positive "R" , right parenthesis StartRoot, left parenthesis, negative StartFraction, "R" negative "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" positive Start integral from 0 to "r" , end integral, 2 pi "x" "d" "x"∫h02π−R−rhz+R−R−rh2+1dz+∫R02πxdx+∫r02πxdx
equals=
219.2 1 1 1 8 5 9 1 9219.211185919
23
Perspective View
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24
Expression 25: theta Subscript, "h" "o" "r" "i" "z" "o" "n" "t" "a" "l" , Baseline equals negative 0.5θhorizontal=−0.5