google can provide all of these
as, I suspect, can your course materials.
What's total perimeter, surface area, volume formula for prismatoid (i.e. cuboid frustum [namely trapezoidal body, rectangle frustum] and wedge)?
Please give me the full formula and the train/stream of thoughts. Both of them I need. Thanks.
3 answers
For Wedges:
Total perimeter: I don't know
Surface/Full Area: S = ab + 1 / 2 ( a + c ) √ ( 4h ^ 2 + b ^ 2 ) + b √ ( h ^ 2 + (a-c) ^ 2
Volume: V
Total perimeter: I don't know
Surface/Full Area: S = ab + 1 / 2 ( a + c ) √ ( 4h ^ 2 + b ^ 2 ) + b √ ( h ^ 2 + (a-c) ^ 2
Volume: V
Sorry, due to computer issues, I press 'enter' key by a mistake, and forgot:
Wedges: V = 1 / 6 bh ( 2a + c )
Cuboid Frustums: C = 2 ( a1 + a2 + b1 + b2 ) + 4c
S = a1b1 + a2b2 + ( a1 + a2 ) l1 + ( b1 + b2 ) l2
V = 1 / 6 h ( S1 + S2 + ( a1 + a2 ) ( b1 + b2 ) )
And: S1 = a1b1, S2 = a2b2, l1 = √ ( ( ( b1 - b2 ) / 2 ) ^ 2 + h ^ 2 ) , l1 = √ ( ( ( b1 - b2 ) / 2 ) ^ 2 + h ^ 2 ) , l2 = √ ( ( ( a1 - a2 ) / 2 ) ^ 2 + h ^ 2, ) c = √ ( ( ( a1 - a2 ) / 2 ) ^ 2 + l1 ^ 2 )
Wedges: V = 1 / 6 bh ( 2a + c )
Cuboid Frustums: C = 2 ( a1 + a2 + b1 + b2 ) + 4c
S = a1b1 + a2b2 + ( a1 + a2 ) l1 + ( b1 + b2 ) l2
V = 1 / 6 h ( S1 + S2 + ( a1 + a2 ) ( b1 + b2 ) )
And: S1 = a1b1, S2 = a2b2, l1 = √ ( ( ( b1 - b2 ) / 2 ) ^ 2 + h ^ 2 ) , l1 = √ ( ( ( b1 - b2 ) / 2 ) ^ 2 + h ^ 2 ) , l2 = √ ( ( ( a1 - a2 ) / 2 ) ^ 2 + h ^ 2, ) c = √ ( ( ( a1 - a2 ) / 2 ) ^ 2 + l1 ^ 2 )
5 answers