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Math Help - 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; March 4th 2010 at 12:34 AM. 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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  5. #5
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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 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 = 1^3:24^3
    =1:13824
    So the actual statue has a volume which is 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 13824\times 1.3 pounds. But marble is heavier than clay, with the same volume of each in the ratio 175:150. We can simplify this (by dividing by 25) to 7:6.

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

    Grandad
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