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Math Help - please help me

  1. #1
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    Question please help me

    i have two maths questions in my homework im stuck on.
    1.an empty 750 ml glass bottle has a mass of 89 grams when it is full of water what is its mass.
    2. here are three cross sections of the same solid. cirlce,triangle and oval. name it
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mellisaj12
    i have two maths questions in my homework im stuck on.
    1.an empty 750 ml glass bottle has a mass of 89 grams when it is full of water what is its mass.
    2. here are three cross sections of the same solid. cirlce,triangle and oval. name it
    1. Water at 4 C has a density of 1 g/mL, so the bottle will have 750 g of water in it. Thus the bottle + water has a total mass of 839 g.

    2. The object is a cone. (I can't draw the pictures, sorry!)

    -Dan
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  3. #3
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by topsquark

    2. The object is a cone. (I can't draw the pictures, sorry!)

    -Dan
    Where's the oval?
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    a big thanks to Dan

    i just want to let Dan know i am thankful for answering my questions. I have never been very good at maths and as my daughter is getting older its becoming more difficult
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Quick
    Where's the oval?
    Imagine the cone is "sitting" on its circular base. Now consider a plane cutting the cone at an angle.

    You can probably get a decent set of cross-section diagrams by looking up "conic sections" on the internet.

    -Dan
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mellisaj12
    i just want to let Dan know i am thankful for answering my questions. I have never been very good at maths and as my daughter is getting older its becoming more difficult
    Always pleased to be of help.

    -Dan
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  7. #7
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    Quote Originally Posted by topsquark
    Imagine the cone is "sitting" on its circular base.
    Now consider a plane cutting the cone at an angle.

    Brilliant, Dan!
    I had difficulty with the "oval" (ellipse) but you made it so obvious.

    Code:
                  A
                  *
                 / \
                /   \
               /     \
              /       *D
             /     *   \
            /   *       \
           / *           \
         B* - - - - - - - *C

    \Delta ABC is a side view of a circular cone (it doesn't have to be "right").

    A slanted plane cut through the plane, passing through B and D,
    . . and the top portion is removed.

    From the front, we see \Delta BCD.

    From the top, we see a circle with diameter BC.

    From the left, we see an ellipse with major axis BD.


    Does this have a name? . . . other than "circular conical wedge"?

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  8. #8
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Soroban

    Brilliant, Dan!
    I had difficulty with the "oval" (ellipse) but you made it so obvious.

    Code:
                  A
                  *
                 / \
                /   \
               /     \
              /       *D
             /     *   \
            /   *       \
           / *           \
         B* - - - - - - - *C

    \Delta ABC is a side view of a circular cone (it doesn't have to be "right").

    A slanted plane cut through the plane, passing through B and D,
    . . and the top portion is removed.

    From the front, we see \Delta BCD.

    From the top, we see a circle with diameter BC.

    From the left, we see an ellipse with major axis BD.


    Does this have a name? . . . other than "circular conical wedge"?

    It probably does. I never did 3D geometry so I'm a little uncertain.

    I appreciate the comment of "brilliant" but I can't take credit for it. Any Intermediate level Mechanics book has a picture of this, owing to motion under an inverse square force law. This diagram shows the different types of orbit due to Newton's Law of Gravitation...the "conic sections." Which means you can get a parabola and a hyperbola as well, given the correct angle for the cross section. (The cone is "doubled" by continuing it through its point.)

    -Dan
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