Expression 15: StartFraction, "n" Over 12 , EndFraction "h" "s" squared co tangent left parenthesis, StartFraction, pi Over "n" , EndFraction , right parenthesisn12hs2cotπn
equals=
168.6 0 6 7 8 5 2 5 8168.606785258
15
Volume by Integration (Polygons)
16
Expression 17: Start integral from 0 to "h" , end integral, StartFraction, "n" Over 4 , EndFraction left parenthesis, negative StartFraction, "s" Over "h" , EndFraction "z" plus "s" , right parenthesis squared co tangent left parenthesis, StartFraction, pi Over "n" , EndFraction , right parenthesis "d" "z"∫h0n4−shz+s2cotπndz
equals=
168.6 0 6 7 8 5 2 5 8168.606785258
17
Volume by Integration (Shells)
18
Expression 19: Start integral from 0 to StartFraction, "s" Over 2 , EndFraction cot left parenthesis, StartFraction, pi Over "n" , EndFraction , right parenthesis , end integral, 2 "n" tangent left parenthesis, StartFraction, pi Over "n" , EndFraction , right parenthesis left parenthesis, negative StartFraction, 2 "h" Over "s" cot left parenthesis, StartNestedFraction, pi NestedOver "n" , EndNestedFraction , right parenthesis , EndFraction "y" positive "h" , right parenthesis "y" "d" "y"∫s2cotπn02ntanπn−2hscotπny+hydy
equals=
168.6 0 6 7 8 5 2 5 8168.606785258
19
Surface Area
Hide this folder from students.
20
Surface Area by Formula
21
Expression 22: StartFraction, "n" "s" Over 4 , EndFraction left parenthesis, "s" cot left parenthesis, StartFraction, pi Over "n" , EndFraction , right parenthesis positive 2 StartRoot, left parenthesis, StartFraction, "s" Over 2 , EndFraction cot left parenthesis, StartFraction, pi Over "n" , EndFraction , right parenthesis , right parenthesis squared positive "h" squared , EndRoot , right parenthesisns4scotπn+2s2cotπn2+h2
equals=
218.9 5 8 7 3 7 8 9 5218.958737895
22
Surface Area by Integration (Polygons)
23
Expression 24: "n" Start integral from 0 to StartFraction, "s" Over 2 , EndFraction cot left parenthesis, StartFraction, pi Over "n" , EndFraction , right parenthesis , end integral, 2 "y" tangent left parenthesis, StartFraction, pi Over "n" , EndFraction , right parenthesis StartRoot, 1 positive left parenthesis, negative StartFraction, 2 "h" Over "s" cot left parenthesis, StartNestedFraction, pi NestedOver "n" , EndNestedFraction , right parenthesis , EndFraction , right parenthesis squared , EndRoot "d" "y" positive "n" Start integral from 0 to StartFraction, "s" Over 2 , EndFraction cot left parenthesis, StartFraction, pi Over "n" , EndFraction , right parenthesis , end integral, 2 "y" tangent left parenthesis, StartFraction, pi Over "n" , EndFraction , right parenthesis "d" "y"n∫s2cotπn02ytanπn1+−2hscotπn2dy+n∫s2cotπn02ytanπndy
equals=
218.9 5 8 7 3 7 8 9 5218.958737895
24
Perspective View
Hide this folder from students.
25
Expression 26: theta Subscript, "h" "o" "r" "i" "z" "o" "n" "t" "a" "l" , Baseline equals negative 0.5θhorizontal=−0.5
