1. Standard memberwittywonka
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    06 Apr '07 03:08
    What is the volume of a right hexagonal prism with each base's perimeter measuring 60 cm and with a height of 5 cm? What about a right octagonal prism with the same measurements?
  2. SubscriberAThousandYoung
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    06 Apr '07 08:01
    Originally posted by wittywonka
    What is the volume of a right hexagonal prism with each base's perimeter measuring 60 cm and with a height of 5 cm? What about a right octagonal prism with the same measurements?
    I could do this, but I suspect it's your homework.
  3. Standard memberwittywonka
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    06 Apr '07 18:35
    Originally posted by AThousandYoung
    I could do this, but I suspect it's your homework.
    Lol...I can do it too. Actually, it was my homework, but it was several chapters ago.

    Here, to prove it, the formula is V=((P*a)/2)*(H)

    The only problem is knowing what those variables mean... 😛
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    06 Apr '07 18:53
    Originally posted by wittywonka
    What is the volume of a right hexagonal prism with each base's perimeter measuring 60 cm and with a height of 5 cm? What about a right octagonal prism with the same measurements?
    Hexagonal prism:

    hexagon side = 10cm.
    hexagon area = 6*10*sqrt(3)/4 = 15*sqrt(3) (6 times the area of an equilateral triangle with side length 10)
    Volume = base*height = 15*sqrt(3)*5 = 75*sqrt(3).


    The octogonal prism can be dealt with in the same way, though the calculations for the area of the base are a little messier.
  5. Standard memberwittywonka
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    06 Apr '07 19:26
    Originally posted by GregM
    Hexagonal prism:

    hexagon side = 10cm.
    hexagon area = 6*10*sqrt(3)/4 = 15*sqrt(3) (6 times the area of an equilateral triangle with side length 10)
    Volume = base*height = 15*sqrt(3)*5 = 75*sqrt(3).


    The octogonal prism can be dealt with in the same way, though the calculations for the area of the base are a little messier.
    Why did you divide by four? I think you only divide by two...
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    06 Apr '07 21:05
    No, but I did miss a square: the area of an equilateral triangle with side length S is S^2*sqrt(3)/4, so the correct numbers would be

    hexagon area = 6*10^2*sqrt(3)/4 = 150*sqrt(3) (6 times the area of an equilateral triangle with side length 10)
    Volume = base*height = 150*sqrt(3)*5 = 750*sqrt(3).
  7. Standard memberDeepThought
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    07 Apr '07 01:061 edit
    Originally posted by GregM
    No, but I did miss a square: the area of an equilateral triangle with side length S is S^2*sqrt(3)/4, so the correct numbers would be

    hexagon area = 6*10^2*sqrt(3)/4 = 150*sqrt(3) (6 times the area of an equilateral triangle with side length 10)
    Volume = base*height = 150*sqrt(3)*5 = 750*sqrt(3).
    Where do you get sqrt(3) from? The area of the triangle is 25*sqrt(2).

    Edit: Posted before checking - I'm thinking of sin(45) 😞
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