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Math Help - Mensuration - Volume and surface area

  1. #1
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    Mensuration - Volume and surface area

    Question: A Well of diameter 3 Meter is dug 14 Meter deep. The earth taken out of it is spread evenly all around it in shape of circular ring of width 4 Meter to form an embarkment. Find the height of the embarkment.

    My answer isnt matching with the books given answer. Please help
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  2. #2
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    Quote Originally Posted by shaurya View Post
    Question: A Well of diameter 3 Meter is dug 14 Meter deep. The earth taken out of it is spread evenly all around it in shape of circular ring of width 4 Meter to form an embarkment. Find the height of the embarkment.

    My answer isnt matching with the books given answer. Please help
    The volume of earth removed is

    v=\pi r^2h=\pi\left(\frac{3}{2}\right)^2(14)=\frac{63\pi  }{2}


    The volume of the enbankment is

    V=\left(\frac{11}{2}\right)^2\pi h-\left( \frac{3}{2}\right)^2\pi h=28\pi h

    Now setting the volumes equal we can solve for h

    28 \pi h = \frac{63 \pi}{2} \iff h =\frac{63 \pi }{2} \cdot \frac{1}{28 \pi}=\frac{63}{56} m

    Okay I think I fixed it.
    Last edited by TheEmptySet; May 16th 2008 at 06:09 PM. Reason: I made a BIG mistake
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    Hmm, your right but i cant figure out wat does it mnean by an embankment here. Can you give me a figuire or so? I couldnt understand the volume of embankment.
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  4. #4
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    Quote Originally Posted by shaurya View Post
    Hmm, your right but i cant figure out wat does it mnean by an embankment here. Can you give me a figuire or so? I couldnt understand the volume of embankment.
    I've attached a rough sketch of the well and it's embankment.
    Attached Thumbnails Attached Thumbnails Mensuration - Volume and surface area-well_embankment.gif  
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