Prof. Templeton Posted November 25, 2008 Report Share Posted November 25, 2008 The Statue of Liberty stands 93 meters tall and has a weight of 200,000 kg. Assuming that it is constucted of a uniform material, how tall would an exact scale model constructed of the same material be if it weighed 1 kg? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 25, 2008 Report Share Posted November 25, 2008 The Statue of Liberty stands 93 meters tall and has a weight of 200,000 kg. Assuming that it is constucted of a uniform material, how tall would an exact scale model constructed of the same material be if it weighed 1 kg? 2150 mm? not sure... im used to the english unit of measure... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 25, 2008 Report Share Posted November 25, 2008 93/200000 meter=0.465 milimeter. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 25, 2008 Report Share Posted November 25, 2008 The Statue of Liberty stands 93 meters tall and has a weight of 200,000 kg. Assuming that it is constucted of a uniform material, how tall would an exact scale model constructed of the same material be if it weighed 1 kg? 1.59m density won't change, so 1 kg give about 1/200,000 of the original volume. Height is propotionally to cube root of the volume. So model height = 93 / ( 200,000)^(1/3) = 1.59028..... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 25, 2008 Report Share Posted November 25, 2008 ok, I'll lead with my chin..... 0.465 mm. then I continue to work it out.... Quote Link to comment Share on other sites More sharing options...
0 Yoruichi-san Posted November 25, 2008 Report Share Posted November 25, 2008 1.59m density won't change, so 1 kg give about 1/200,000 of the original volume. Height is propotionally to cube root of the volume. So model height = 93 / ( 200,000)^(1/3) = 1.59028..... I'm with woon ;P. Sneaky dimensional analysis! Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted November 25, 2008 Author Report Share Posted November 25, 2008 1.59m density won't change, so 1 kg give about 1/200,000 of the original volume. Height is propotionally to cube root of the volume. So model height = 93 / ( 200,000)^(1/3) = 1.59028..... You are right on woon. Good job. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 25, 2008 Report Share Posted November 25, 2008 i guess that's only true if the statue of liberty is a cube..lol...density=density (no change) ... hence m/v=m/v... 200000/(93*width*length)=1/(X*width2*length2) if width = length = height then X^3=93^3/200000 X=93/200000^1/3 But it's not a cube... it has infinite solution the correct answer is : X=93 *( original width)^2)/200000*(width after size reduced)^2 think about it Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted November 25, 2008 Author Report Share Posted November 25, 2008 i guess that's only true if the statue of liberty is a cube..lol...density=density (no change) ... hence m/v=m/v... 200000/(93*width*length)=1/(X*width2*length2) if width = length = height then X^3=93^3/200000 X=93/200000^1/3 But it's not a cube... it has infinite solution the correct answer is : X=93 *( original width)^2)/200000*(width after size reduced)^2 think about it It doesn't have to be a cube. All dimensions are reduced by a factor of x, so it's x*x*x=x3. The ratio of the mass between the Statue and the model is 200000:1, since the density doesn't change, the volume of the Statue is 200000 times that of the model. Therefore all length scales of the original Statue are 200000(1/3)=58.48 times larger than the scale model. 93 meters / 58.48 = 1.59 meters tall for the scale model. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 25, 2008 Report Share Posted November 25, 2008 Whattay know? I got what Woon got. I'm still trying to figure out how to show my work in this format. Quote Link to comment Share on other sites More sharing options...
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Prof. Templeton
The Statue of Liberty stands 93 meters tall and has a weight of 200,000 kg. Assuming that it is constucted of a uniform material, how tall would an exact scale model constructed of the same material be if it weighed 1 kg?
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