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Math Help - Frustum of Regular Pyramid..FlowerPot

  1. #1
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    Frustum of Regular Pyramid..FlowerPot

    The flowerpot shown in the sketch has a uniform thickness of 3in. and is 1ft high. Find the amount of material necessary to construct 1000 such pots. (Neglect the drain in the bottom)



    What I did is get the volume of the bigger frustum which results to:

    V = [h(18^2 + 12^2 + sqrt (18 * 12))]/3
    V = 1930.79 cu. in

    I don't know now the next step...

    the answer should be 1098 cu. ft.

    Help please THANKS!
    Last edited by cutiemike1; September 6th 2010 at 04:51 AM.
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  2. #2
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    Inner dimensions will be 12 in, 6 in and height 9 in. Find the volume V' of the inneer space.

    V - V' will give the volume of the material.
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  3. #3
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    Quote Originally Posted by sa-ri-ga-ma View Post
    Inner dimensions will be 12 in, 6 in and height 9 in. Find the volume V' of the inneer space.

    V - V' will give the volume of the material.
    It will not come up with the right answer. By the way thanks for help.
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  4. #4
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    Hello, cutiemike1!

    Two problems: You are misreading the volume formula.
    . . . . . . . . . . .I don't agree with the given answer.


    The flowerpot shown in the sketch has a uniform thickness of 3in. and is 1ft high.
    Find the amount of material necessary to construct 1000 such pots.



    The answer should be 1098 cubic feet. . ??




    The volume of a frustum of a pyramid is: . V \;=\;\dfrac{h}{3}\left(B_1 + B_2 + \sqrt{B_1B_2}\right)
    where: h is the height of the frustum
    . . . . . and B_1,B_2 are the areas of the two bases.



    The outer frustum has: . \begin{Bmatrix} h &=& 12 \\ B_1 &=& 18^2 &=& 324 \\ B_2 &=& 12^2 &=& 144 \end{Bmatrix}\;\text{ inches}

    The outer volume is: . V_o \;=\;\dfrac{12}{3}\left(324 + 144 + \sqrt{324\cdot144}\right)

    . . . . . . . . . . . . . . . . . . =\;4(468 + \sqrt{46,\!656})  \;=\;4(468 + 216)

    . . . . . . . . . . . . . . . . . . =\;4(684) \;=\;2736\text{ in}^3



    The inner frustum has: . \begin{Bmatrix}h &=& 9 \\ B_1 &=& 12^2 &=& 144 \\ B_2 &=& 6^2 &=& 36 \end{Bmatrix}\;\text{ inches}

    The inner volume is: . V_i \;=\;\frac{9}{3}\left(144 + 36 + \sqrt{144\cdot36}\right)

    . . . . . . . . . . . . . . . . . . =\; 3(180 + \sqrt{5184}) \;=\;3(180 + 72)

    . . . . . . . . . . . . . . . . . . =\;3(252) \;=\;756\text{ in}^3



    One pot requires: . 2736 - 756 \:=\:1980\text{ in}^3 of material.

    A thousand pots will require: . 1,\!980,\!000\text{ in}^3 of material.

    . . which equals: . \dfrac{1,\!980,\!000}{1728} \;=\;1145\frac{5}{6}\text{ ft}^3 of material.
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  5. #5
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    Thank You Sir Soroban...Sorry for the late reply to this thread.
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  6. #6
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    HI! i think the B2 of the inner frustum is 7.5 which results to a final answer of 1079.42 cubic feet.
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  7. #7
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    confused

    i am really confused with this problem. my prof really argue that the answer on the book solid mensuration which happens to be bland and kern he said though the book ages the answer dont .. lol he really stands that the answer is 1098.0 cu.ft. which is really annoyingly unsolvable
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