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January 28th, 2015, 10:50 PM  #1 
Senior Member Joined: Jan 2012 Posts: 745 Thanks: 7  Calculate the mass
Calculate the mass, in kg, of a rectangular sheet of metal 15.7 cm long and 12.9 cm wide, if its mass is 38.1 g per cm2. Area = $15.7\times12.9 =(202.53cm^2)$ 202.53cm = $\frac{202.53}{38.1}$ = 5.31574803 g = $\frac{5.3157}{1000}$ = 0.005316kg 
January 29th, 2015, 01:32 AM  #2 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,164 Thanks: 736 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
You divided it when you should have multiplied it. Total mass = mass per unit area $\displaystyle \times$ total area. 
January 29th, 2015, 04:34 AM  #3  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  Quote:
That obviously isn't true! And, of course, as Benit13 said, you divided when you should have multiplied. You could have recognized that your self by looking at the units. Area is in $\displaystyle cm^2$, mass is in g, and its density (not mass) is in $\displaystyle \frac{g}{cm^2}$. To divide by a fraction, we "invert" the fraction and multiply: $\displaystyle (cm^2)(\frac{cm^2}{g})= \frac{cm^4}{g}$ will NOT give "g". But multiplying gives $\displaystyle (cm^2)(\frac{g}{cm^2}= g$ because the "$\displaystyle cm^2$" terms cancel. Quote:
 

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