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course Mth 173
6/23/13~8:20PM
If a sand pile 4 meters high has a mass of 146000 kg, then what would we expect to be the mass of a geometrically similar sand pile 14 meters high? If the sand pile is 4 meters high with a mass of 146000 kg, the formula
y=kx^2 can be applied
146,000 = a (4)^3
146,000 = a (64)
2281.25 = a
y=2281.25(14)^3
y=2281.25(2744)
y= 6,259,750 kg
Using the differential estimate the mass of sand required to increase the height of the pile from 4 meters to 4.03 meters.
Differential is as follows -->
y=ax^3
y’=3ax^2
y’=3(2281)x^2
y’=6843x^2 this is the rate of mass change with respect to x
y’(4)=6843(3^2)
y’(4)=109,488 kg/m
Change in height=4.03 - 4=.03m
109,488 kg/m * .03m =3284.64 kg
146,000 kg + 3284.64 kg=149,284.64 kg (mass at 4.03m)
&#This looks very good. Let me know if you have any questions. &#