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course Mth 271

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? Using the differential estimate the mass of sand required to increase the height of the pile from 4 meters to 4.03 meters.146,000 kg = k(4^3)

146,000kg = 64k

2281.25 kg = k

3(2281.25 kg)(4^2) = 109,500 kg

3(2281.25 kg)(4^2)*.03 = 3285 kg

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Good.

You should include the reasons for these calculations.

The derivative of x^3 is 3 x^2, so the derivative of k x^3 is k * 3 x^2 = 3 k x^2.

The derivative is the rate of change of mass y = k x^3 with respect to height x. So when the derivative is multiplied by the .03 meter change in x, you get the approximate change in the mass y.
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