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  1. #1
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    Exclamation I need help!

    Approximately 118 mi wide and 307 mi long and averaging 279 ft in depth, Lake Michigan is the second-largest Great lake by volume. Estimate its volume of water in m3. (Note that 2.54 cm = 1 inch and 5280 feet = 1 mile)
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  2. #2
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    Hello, babygirl!

    This involves converting units . . . can you do that?


    Approximately 118 mi wide and 307 mi long and averaging 279 ft in depth,
    Lake Michigan is the second-largest Great lake by volume.
    Estimate its volume of water in m.
    (Note that 2.54 cm = 1 inch and 5280 feet = 1 mile)

    Volume is Length x Width x Height (Depth).

    So we have: . V \;= \; 118\text{ miles} \times 307\text{ miles} \times 279\text{ feet}

    Converting miles to meters and feet to meters, we have:
    . . V\;=\;189,902.59 \times 494,068.61 \times 85.04 \;=\;7.9778870234 \times 10^{12} m.


    The volume of Lake Michigan is about 8 \times 10^{12} (eight trillion) cubic meters.

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  3. #3
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    Just asking, where'd that 10 come from? Meaning like the answer is 7978870233866.559496 so where'd you get the 10 from? shouldn't it be 10 razed to 6? Sorry but I'm confused.. I'm a Math rookie...

    Btw, what are the values for converting Miles to Metres?
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  4. #4
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    Quote Originally Posted by Soroban
    Hello, babygirl!

    This involves converting units . . . can you do that?



    Volume is Length x Width x Height (Depth).

    So we have: . V \;= \; 118\text{ miles} \times 307\text{ miles} \times 279\text{ feet}

    Converting miles to meters and feet to meters, we have:
    . . V\;=\;189,902.59 \times 494,068.61 \times 85.04 \;=\;7.9778870234 \times 10^{12} m.


    The volume of Lake Michigan is about 8 \times 10^{12} (eight trillion) cubic meters.

    I would have thought a better approximation would treat the lake as an ellipse
    rather than a rectangle. This would result in an area \pi/4 times that of the
    corresponding rectangle, and as we are given an average depth rather than
    maximum depth the volumes would scale by the same factor. This would
    reduce the estimated volume to \approx 6 \times 10^{12}\ m^3.

    RonL

    By the way the claimed volume is \approx 4.9 \times 10^{12}\ m^3
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  5. #5
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    Quote Originally Posted by Ruler of Hell
    ...
    Btw, what are the values for converting Miles to Metres?
    Hello,

    have a look here: http://en.wikipedia.org/wiki/Conversion_factor

    1 mile = 1609.344 metres

    Greetings

    EB
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