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Thread: Scale model - volume

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    Scale model - volume

    An artist plans to make a large sculpture of a person out of solid marble. She first makes a small scale model out of clay, using a scale of 1 inch = 2 feet. The scale model weighs 1.3 pounds. Assuming that a cubic foot of clay weighs 150 pounds and a cubic foot of marble weighs 175 pounds, how much will the large marble sculpture weigh? Explain your reasoning.

    I am stuck here, can anyone get me started in the right direction?
    Last edited by mr fantastic; Mar 3rd 2010 at 11:34 PM. Reason: Changed post title
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    An artist plans to make a large sculpture of a person out of solid marble. She first makes a small scale model out of clay, using a scale of 1 inch = 2 feet. The scale model weighs 1.3 pounds. Assuming that a cubic foot of clay weighs 150 pounds and a cubic foot of marble weighs 175 pounds, how much will the large marble sculpture weigh? Explain your reasoning.
    if 1 cubic ft of clay weighs 150 and the model weighs 1.3, then the model is 1.3/150 cubic feet. multiply by 12 to get in cubic inches.sp its 15.6/150 cubic inches.
    next, if the scale is 1 in= 2 ft, then 1 cubic inch= 8 cubic ft. so, multiply 15.6/150 by 8= 124.8/150 cubic ft.
    now multiply by 175, the weight of a cubic ft of marble. so the answer would be about 145.6 pounds
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    I am not following exactly...
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    Is this correct? I am not following the conversions
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    Hello igottaquestion
    Quote Originally Posted by igottaquestion View Post
    An artist plans to make a large sculpture of a person out of solid marble. She first makes a small scale model out of clay, using a scale of 1 inch = 2 feet. The scale model weighs 1.3 pounds. Assuming that a cubic foot of clay weighs 150 pounds and a cubic foot of marble weighs 175 pounds, how much will the large marble sculpture weigh? Explain your reasoning.

    I am stuck here, can anyone get me started in the right direction?
    This question is all about ratios.

    When dealing with a scale which has mixed units (in this case feet and inches), the first thing you need to do is to convert to just one set of units. So, if 1 inch represents 2 feet, that's 1 inch represents 24 inches. So the scale is $\displaystyle 1:24$.

    Next, you need to know that, to find the ratio of corresponding areas, you will square the numbers in the ratio; and to find the ratio of corresponding volumes you will cube them. Well, it's the volumes that we're dealing with here, so we cube the numbers to get:
    Ratio of volumes $\displaystyle = 1^3:24^3$
    $\displaystyle =1:13824$
    So the actual statue has a volume which is $\displaystyle 13824$ times as big as the model. (Sounds a lot, but it's true!)

    So if the statue were made of clay, its weight would be $\displaystyle 13824\times 1.3$ pounds. But marble is heavier than clay, with the same volume of each in the ratio $\displaystyle 175:150$. We can simplify this (by dividing by $\displaystyle 25$) to $\displaystyle 7:6$.

    Therefore the actual weight of the statue is $\displaystyle \frac76\times13824\times1.3 $ pounds. And that's about $\displaystyle 20966$ pounds, or about $\displaystyle 9.36$ tons. It must be quite a large statue!

    Grandad
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